We present the double-pass second-harmonic generation (SHG) of picosecond pulses with a custom-poled potassium titanyl phosphate (KTP) nonlinear crystal. The average output power of 466 mW at central wavelength of 515.7 nm is obtained with the input of 1.2 W fundamental laser pulses. Compared to the highest conversion efficiency of 29.1% in the single-pass SHG, the conversion efficiency in the double-pass SHG is increased to 38.8%. Moreover, the average RMS stability of 0.67% in 2 hours and high beam quality (M2 < 1.10) of the second-harmonic pulses is observed. The presented results provide an efficient method to enhance the conversion efficiency of SHG for picosecond pulses.