A sandwich composite consisting of one layer of ferromagnetic shape memory Ni-Mn-Ga crystal plate bonded between two layers of piezoelectric PVDF polymer film was fabricated, and its magnetic field-induced strain (MFIS) and magnetoelectric (ME) effects were investigated, together with a monolithic Ni-Mn-Ga crystal, as functions of magnetic fields and mechanical load. The load-free dc- and ac-MFISs were 0.35 and 0.05% in the composite, and 5.6 and 0.3% in the monolithic crystal, respectively. The relatively smaller load-free MFISs in the composite than the monolithic crystal resulted from the clamping of martensitic twin-boundary motion in the Ni-Mn-Ga plate by the PVDF films. The largest ME coefficient (αE) was 0.58 V/cm·Oe at a magnetic bias field (HBias) of 8.35 kOe under load-free condition. The mechanism of the ME effect originated from the mechanically mediated MFIS effect in the Ni-Mn-Ga plate and piezoelectric effect in the PVDF films. The measured αE-HBias responses under different loads showed good agreement with the model prediction.