  We have investigated the structural and magnetic properties of a new cubic
spinel LiZn$_{2}$V$_{3}$O$_{8}$ (LZVO) through x-ray diffraction, dc and ac
susceptibility, magnetic relaxation, aging, memory effect, heat capacity and
$^{7}$Li nuclear magnetic resonance (NMR) measurements. A Curie-Weiss fit of
the dc susceptibility $\chi_{\mathrm{dc}}$($\mathit{T}$) yields a Curie-Weiss
temperature $\mathrm{\theta}_{\mathrm{CW}}$ = -185 K. This suggests strong
antiferromagnetic (AFM) interactions among the magnetic vanadium ions. The dc
and ac susceptibility data indicate the spin-glass behavior below a freezing
temperature $T_{f}$ $\simeq$ 3 K. The frequency dependence of the $T_{f}$ is
characterized by the Vogel-Fulcher law and critical dynamic scaling behavior or
power law. From both fitting, we obtained the value of the characteristic
angular frequency $\omega_{0}$ $\approx$ 3.56$\times$10$^{6}$ Hz, the dynamic
exponent $\mathit{zv}$ $\approx$ 2.65, and the critical time constant
$\tau_{0}$ $\approx$ 1.82$\times$10$^{-6}$ s, which falls in the conventional
range for typical cluster spin-glass (CSG) systems. The value of relative shift
in freezing temperature $\delta T_{f}$ $\simeq$ 0.039 supports a CSG ground
states. We also found aging phenomena and memory effects in LZVO. The
asymmetric response of the magnetic relaxation below $T_{f}$ supports the
hierarchical model. Heat capacity data show no long-range or short-range
ordering down to 2 K. Only about 25% magnetic entropy change $(\Delta
S_{\mathrm{m}})$ signifies the presence of strong frustration in the system.
The $^{7}$Li NMR spectra show a shift and broadening with decreasing
temperature. The spin-lattice and spin-spin relaxation rates show anomalies due
to spin freezing around 3 K as the bulk magnetization.
