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But there were dragons in the wastes beyond; and after many years they became strong again and multiplied, and they made war on the Dwarves and plundered their works.
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So the rumour of the wealth of Erebor spread abroad and reached the ears of the dragons, and at last Smaug the Golden, greatest of the dragons of his day, rose and without warning came against King Thrór and descended on the Mountain in flames.
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Both quotes are from Appendix A, Durin's Folk. Therefore, Smaug was not the last Dragon, but the last great dragon and the greatest of the time.