We study the dependence of the critical temperature of a two-band d-wave superconductor on the intensity of an odd parity hybridization between these bands. We consider a two-dimensional (2D) system in the presence of an attractive inter-band interaction. The odd-parity k-dependent hybridization is appropriate to describe mixing of electronic states arising from orbitals with angular momenta that differ by an odd number, such as, sp, pd or df bands. We show that increasing the strength of the odd-parity hybridization enhances superconductivity and also changes the nature of superconductivity from a Bardeen-Cooper-Schrieffer (BCS) type of pairing to a Bose-Einstein condensation (BEC) characteristic of a strong coupling regime, even for weak-couplings. This crossover can also be driven by increasing the binding energy, that appears in the two-body interaction of these 2D systems. Finally, we investigate the effect of the variation in the carrier density on the superconducting phase diagram.