To suppress spectral drift in lengthy gamma spectrum measurements, a convenient and practical spectrum stabilization method with software-only adjustment is studied. The gamma energy spectra are recorded in consecutive small time intervals. The drifts in different time intervals relative to the first reference spectrum are estimated with a full spectrum nonlinear optimization technique, and the drifted spectra are corrected and accumulated to form a drift-free spectrum. This method needs neither hardware adjustment such as high voltage or electronics gain, nor peak location. Presented experimental results show that the stabilization accuracy can be significantly improved using this approach.