We present a comprehensive analysis (photometric and kinematical) of poorly studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia~DR2 database. By determining the membership probabilities of stars, we identified 624 most probable members with membership probability higher than $50%$ by using proper motion and parallax data taken from Gaia~DR2. The mean proper motion of the cluster is obtained as $mu_{x}=-8.83pm0.01$ and $mu_{y}=1.49pm0.006$ mas yr$^{-1}$. We find the normal interstellar extinction towards the cluster region. The radial distribution of members provides a cluster radius of 7.75 arcmin (5.63 pc). The estimated age of $1600pm180$ Myr indicates that NGC 4337 is an old open cluster with a bunch of red giant stars. The overall mass function slope for main-sequence stars is found as $1.46pm0.18$ within the mass range 0.75$-$2.0 $M_odot$, which is in fair agreement with Salpeters value (x=1.35) within uncertainty. The present study demonstrates that NGC 4337 is a dynamically relaxed open cluster. Using the Galactic potential model, Galactic orbits are obtained for NGC 4337. We found that this object follows a circular path around the Galactic center. Under the kinematical analysis, we compute the apex coordinates $(A, D)$ by using two methods: (i) the classical convergent point method and (ii) the AD-diagram method. The obtained coordinates are: $(A_{conv}, D_{conv})$ = (96$^{textrm{o}}$.27 $pm$ 0$^{textrm{o}}$.10, 13$^{textrm{o}}$.14 $pm$ 0$^{textrm{o}}$.27) $&$ $(A_circ, D_circ)$ = (100$^{textrm{o}}$.282 $pm$ 0$^{textrm{o}}$.10, 9$^{textrm{o}}$.577 $pm$ 0$^{textrm{o}}$.323) respectively. We also computed the Velocity Ellipsoid Parameters (VEPs), matrix elements ($mu_{ij}$), direction cosines ($l_j$, $m_j$, $n_j$) and the Galactic longitude of the vertex ($l_2$).
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