Yes, the Qur'an contains many prophecies about the future. Many of these have already proved true, and we confidently expect that the others will also come to pass in due time. In addition, no statement in the Qur'an has ever proved to be false.
Let us see some examples of Qur'anic prophecies that has already been fulfilled. One example is a prophecy that occurs in Surah 30 of the Qur'an. In the first six verses Allah promised that the Romans who had just been defeated in the year 615 C.E. would turn around and win a decisive victory within nine years. At the time this statement was made, no human could envision how it could come to pass. The Romans had been so soundly defeated that no hope was left that they could make a comeback within such a short period of time. The disbelievers mocked at the Muslims over this passage in the Qur'an because they thought the prophecy would surely fail. One man, Ummayah bin Khalaf by name, even placed a bet of a hundred camels that the prophecy would fail. Abu Bakr, the closest follower of the prophet, on whom be peace, took up that challenge because he was sure that the word of God could never fail. True enough, within the specified period, in the year 624 CE, the Romans confronted the Persians in battle at a place called Issus. The Romans won their decisive victory exactly as prophecised in the Qur'an, and Abu Bakr, may Allah be pleased with him, won the bet of one hundred camels. In the meantime, however, revelation from Allah had prohibited gambling, so the prophet directed Abu Bakr to give away the camels to the poor and needy.
So the prophecy was fulfilled. But there is more to this. The same verses contain yet another prophecy. It says that while the Romans are winning their victory, the believers in the Qur'an will rejoice in the victory granted by Allah. We know from history that in that very year the Muslims were threatened with total annihilation, but Allah rescued them. The Muslims had been driven out of Mecca, their hometown. Now they found safe haven in Medina. But the unbelievers could not rest knowing that the Muslims were free to practice their faith somewhere else. So they marched against the Muslims with an army of one thousand men fully equipped for battle. The Muslims mustered the best defense they could, a mere 313 men lacking suitable equipment for battle. From a human point of view, the greater force would win, but the help of Allah was with the small group of believers. Miraculously, the believers won, and the Qur'anic prophecy was fulfilled despite all odds. The unfolding of this double prophecy proves beyond doubt that the Qur'an could not have been authored by any human being.
Another prophecy occurs in Surah 111 of the Qur'an. That Surah states that a certain man and his wife will perish as unbelievers. This was uttered at a time when no one but God could say who will or will not become believers later on. Many of the most severe opponents in the early days became devoted followers in later days. But not this couple. They tried everything to oppose, ridicule, and disprove the Qur'an. One would expect that they would also pretend to become believers just to throw doubt on the accuracy of the Qur'an. But they did not apply this obvious strategy. What prevented them, if not the power of God and the truth of His word?
In this way many prophecies were fulfilled, and not one has ever failed. This gives us every reason to place our full confidence in the book of God.