Two operating modes, independent self-mode-locking and cross-mode-locking, are presented in a two-beam-pumped double-cavity dual-wavelength femtosecond Ti:sapphire laser. Synchronization of femtosecond and picosecond laser pulses is achieved by properly adjusting the cavity length matching and distributing the pump laser powers in the two laser cavities, and moreover, a timing jitter of 517 fs between femtosecond and picosecond pulses is obtained, with wavelength tuning ranges around 36 and 22 nm in the femtosecond and picosecond cavities, respectively.