  We report here the structural, electrical and magnetic properties of as-cast
V$_{1-x}$Zr$_x$ alloys ($x$ =0 - 0.4) at low temperatures. We observe that all
the alloys undergo successive peritectic and eutectic reactions during cooling
from the melt which leads to the formation of five phases, namely, a body
centred cubic $\beta$-V phase, two phases with slightly different compositions
having face centred cubic ZrV$_2$ structure, a hexagonal closed packed
$\alpha$-Zr phase, and the $\beta$-Zr precipitates. The amount of each phase is
found to be dependent on the concentration of zirconium in vanadium. The
$\beta$-V and ZrV$_2$ phases show superconductivity below 5.3~K and 8.5~K
respectively. We show that the critical current density is large for V-rich
V$_{1-x}$Zr$_x$ alloys with $x >$ 0.1. The grain boundaries generated from the
eutectic reaction, and the point defects formed due to the variation in the
composition are found to be responsible for the pinning of flux lines in low
and high magnetic fields respectively. Our studies reveal that the choice of
the composition and the heat treatment which leads to eutectic reaction are
important in improving the critical current density in this alloy system.
