The tunable bandwidth and the parametric bandwidth of periodically poled LiNbO3 (PPLN) based on picosecond optical parametric amplifier with different noncollinear geometries are investigated theoretically and numerically. By utilizing an noncollinear geometry recommended by ourself and setting both the noncollinear angle θ between the wave vectors of the pump and the quasi-phase-matching grating and the grating period of PPLN at optimal values, broad and stable tunable bandwidth can be obtained. An expression is proposed to calculate the optimal grating period for PPLN. By expanding the wave-vector mismatch in a Taylor series and retaining terms through first order, second order and third order, respectively, three equations are presented to determine the parametric bandwidth. The results calculated from these equations are analyzed and compared with that calculation by employing the wave-vector mismatch directly, and then the effect of high order series on the parametric bandwidth is studied. At the end, a feasible scheme is presented to determine the working temperature and noncollinear angle α, maximize the tunable bandwidth and parametric bandwidth, and simplify the experimental operation.