A picosecond beam with Gaussian profile was efficiently shaped into a super-Gaussian profile beam by a circular aperture combined with a spatial filter-image relaying system. By studying the influence of the size of the filter aperture on the shaping effect in the spatial filter-image relaying system, the experimental results for maintaining the filling factor of the super-Gaussian beam greater than 0.76 in the propagation distance of 200 mm to 500 mm was obtained, and the corresponding efficiency of this beam shaping method was over 32%. Then, the beam with a super-Gaussian distribution was amplified. By using the thermal lens of semiconductor laser side pumped Nd:YAG crystal to replace the lens in the 4F image relaying system, the structure of the super-Gaussian picosecond laser amplification system can be simplified. After double-passing the single Nd:YAG crystal, a picosecond super-Gaussian profile beam with a near-field fill factor of 0.72, 1 kHz repetition rate, 11 ps duration and 3.0 mJ single-pulse energy was obtained, and the corresponding peak power intensity was up to 8 GW/cm2.