Single crystals of the perovskite-type $3d^{1}$ metallic alloy system Ca$_{1-x}$Sr$_x$VO$_3$ were synthesized in order to investigate metallic properties near the Mott transition. The substitution of a Ca$^{2+}$ ion for a Sr$^{2+}$ ion reduces the band width $W$ due to a buckling of the V-O-V bond angle from $sim180^circ$ for SrVO$_3$ to $sim160^circ$ for CaVO$_3$. Thus, the value of $W$ can be systematically controlled without changing the number of electrons making Ca$_{1-x}$Sr$_x$VO$_3$: one of the most ideal systems for studying band-width effects. The Sommerfeld-Wilsons ratio ($simeq2$), the Kadowaki-Woods ratio (in the same region as heavy Fermion systems), and a large $T^{2}$ term in the electric resistivity, even at 300 K, substantiate a large electron correlation in this system, though the effective mass, obtained by thermodynamic and magnetic measurements, shows only a systematic but moderate increase in going from SrVO$_3$ to CaVO$_3$, in contrast to the critical enhancement expected from the Brinkmann-Rice picture. It is proposed that the metallic properties observed in this system near the Mott transition can be explained by considering the effect of a non-local electron correlation.