A diode-end-pumped dual-wavelength mode-locked laser based on Nd:LuYSiO5 crystal is demonstrated. With a SESAM, simultaneous mode locking at the 1075.8 nm and 1078.1 nm is achieved and the dual-wavelength mode locked pulses have a pulse width of 8.9 ps. Due to frequency beating, ultrahigh repetition rate ultrafast pulses with 997 fs pulse width and 0.59 THz repetition rate are further formed. Under 12.7 W absorbed pump power 1.7 W mode-locked output power was obtained, the slope efficiency of the mode locked laser was 24.3%.