The exclusive semileptonic decays like D0 and B0 mesons are studied in the framework of a relativistic field-theoretic quark model, where translationally invariant hadronic states are described by constituent quark field operators satisfying equal time algebra and a harmonic oscillator wave function. The present estimations to the relevant form factors and their q2 dependence, without any free parameters, show a reasonable agreement with the available experimental measurements and Heavy Quark Effective Theory (HQET) and other model calculations. Further, the calculated decay widths and their ratios, and the polarization ratios for decay processes also have a reasonable agreement with the available experiments and other model estimations.