In this study, orientation dependences of (p)s(11), (p)s(12), (p)epsilon(33) and d(31) for piezoelectric phase were investigated along arbitrary directions using relative experimental data and original matrices for AlN with point group of 6mm. Then, effects of various orientations of piezoelectric phase on magnetoelectric coefficient of AlN-FeCoSiB laminated multiferroic composites were studied. It was found that (p)s(11) is a constant while (p)s(12), (p)epsilon(33) and d(31) exhibit high dependence on crystal orientations with their MAX values existing along [001]-axis. The magnetoelectric coefficient (E33) increases with decreased angle apart from c-axis of AlN in range of 90 degrees-0 degrees; the MAX (E33)=5405mV/cm Oe exists in AlN vertical bar [001]FeCoSiB. Along specific preferred orientations of piezoelectric phase, twofold-fivefold of enhancement of (E33) can be obtained compared to randomly arranged composites. Volume fraction is found to be independent of orientations of component phases, and the volume fraction for magnetic phase f around 0.75 obtains the largest (E33). The results suggest an approach of enhancing magnetoelectric coefficient of composite multiferroic materials through crystal-orientation controls of single crystals or textured ceramics.