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Once The Doctor told Rose that his planet was destroyed before its time. They were at war. He was emotional too just to show how much he missed his planet.
The Doctor is a Time Lord but he didn't talk like a Time Lord. Why can't he save his planet from destruction before time?
The events which caused the destruction of Gallifrey are known as the Last Great Time War. We don't know many of the details of the War (it happened off-screen between the first adventure of the Eighth Doctor and the revival of the series with the Ninth Doctor), but it was a time-travel battle between Time Lords and Daleks, with many other participants.
The LGTW featured efforts of both races to preemptively destroy each other (including at least one semi-successful attempt by the Fourth Doctor). Messing about with time on such a grand scale created paradoxes and monstrosities and was set to rip apart all of history. To end it, the Doctor used something called the Moment. This ended the conflict, but also time-locked the War. It is speculated that everything which was part of the Time War (including Gallifrey, the Daleks, and many other places/creatures) was not physically destroyed, just sealed off from the rest of space and time, effectively sealing the War in a pocket universe.
Because the Last Great Time War is time-locked, this means its events cannot be revisited, even through use of the TARDIS. A handful of creatures/objects have passed through the time lock, but it has dire consequences when it works at all. Dalek Caan managed, at the cost of his sanity and by we know not what means, to enter the time lock and then exit it with Davros. The entire might of the Time Lord empire within the time-lock was sufficient to pass a sound and a small object out into the post-war future, and they could then use this as a link to pull their planet out of the time-lock entirely--but only with significant help from outside, including an entire planet of identical and insane Time Lords on the outside lending their aid.
So the Doctor can't travel through time to save his planet because he purged it from the timeline in order to save the history of the entire universe.
EDIT: The events of The Day of the Doctor have done nothing to substantially change this answer. We're more confident that The Moment was probably responsible for the locking of the LGTW, but we still don't know any of its particulars. The speculation that Gallifrey is locked in a pocket universe is confirmed, but the rest of the War's participants/time periods/locations must have had something similar done to them (probably by The Moment of its own accord, because the Warth Doctor didn't press the Big Red Button) or the Cult of Skaaro --among others-- wouldn't have found traveling to and from those events so difficult.
including an entire planet of identical and insane Time Lords on the outside lending their aid bit? AIUI, The Doctor and The Master are the only Time Lords outside the time locked pocket universe (that we know of yet), yet the TL's on Gallifrey were able to pop open the tunnel using just the drumming sound in The Master's head (and the diamond). Where did this entire planet of insane TLs come from? What did I miss???