The objective of this paper is to apply the technique of asymptotic homogenization to determine the effective elastic, piezoelectric and dielectric moduli of a laminated piezocomposite medium with a periodic structure. Each periodic cell of the medium can possess any finite number of piezoelectric layers. The general formulae obtained are a generalization of those that appear in chapter 5 of Pobedria (Pobedria, B. E. (1984) Mechanics of Composite Materials. Moscow State University Press, Moscow (in Russian)) and involve both cases of Newnham's connectivity theory (Newnham, R. E., Skinner, D. P. and Cross, L. E. (1978) Connectivity and piezoelectric-pyroelectric composites. Materials Research Bulletin 13, 525-536) for layered piezoelectric media. We calculate explicitly overall effective characteristics for three examples of such layered media. For the particular case of a binary layered medium, connected in parallel, with transversely isotropic constituents such formulae transform exactly to the formulae for effective constants obtained by Benveniste et al. (1992) in which a different method of homogenization was used. Finally, we apply these results to a piezocomposite material and obtain new piezoelectric with better global properties for hydrophone applications.