We study the extensional vibration of composite multiferroic piezoelectric semiconductor (PS) nanoharvester driven via a time-harmonic magnetic field. A theoretical analysis about working performances of device is performed based on zero-order plate equations with surface and nonlocal effects, consisting of a nonlinear magneto-mechanical coupling constitutive model for giant magnetostrictive material Terfenol-D and a linear phenomenological theory of PS material ZnO. Numerical results indicate that the basic bahaviors (including resonant frequency, bandwidth characteristic, magneto-electric (ME) coupling effect, output power and energy conversion efficiency) of the nanoharvester, can be dramatically improved through circuit types, semiconduction, external magnetic field, pre-stress and surface effect. This work is essential and crucial for understanding the size-dependent and nonlinear mechanical behaviors of multiferroic PS nanodevices under the extremely complex magnetic field and pre-stress field environments.