No. From "Rose" to "Utopia" (when he encountered the Master), he believed that he was the last surviving Time Lord. After the Master died in "Last of the Time Lords", the Doctor again thought this, except for a short period during "The End of Time" when the Master was resurrected only to be drawn back into the last day of the time-locked Last Great Time War.
However, in "The Day of the Doctor", he learned that he had not, in fact, destroyed Gallifrey & the Time Lords to end the Time War; instead, he had removed them from the universe & sequestered them in a "pocket universe". After that, he thought he was the only Time Lord still in the main universe, until he encountered Missy (a female incarnation of the Master, who somehow got back out of the Time War again) in "Dark Water".