  We report $^{75}$As- and $^{51}$V-nuclear magnetic resonance (NMR)
measurements on the iron-based superconductor Sr$_2$VFeAsO$_3$ with alternating
stacks structure. We find that the $^{75}$As nuclear spin-spin relaxation rate
($1/T_2$) shows a pronounced peak at $T_N$ = 165 K, below which the resonance
peak shifts to a higher frequency due to the onset of an internal magnetic
field. The $^{51}$V spectrum does not shift, but is broadened below $T_N$. We
conclude that the Fe electrons oder antiferromagnetically below $T_N$ with a
magnetic moment $m_{Fe}$ $\sim$ 0.4 $\mu_B$. Application of external pressure
up to 2.4 GPa reduces $T_N$ in a rate of $-$40 K/GPa, and enhances the
superconducting transition temperature $T_c$ in a rate of 2 K/GPa. The
pressure-temperature phase diagram for Sr$_2$VFeAsO$_3$ shows that
superconductivity coexists with antiferromagnetism over a wide pressure range
with an unprecedented high $T_c$ up to 36.5 K.
