  We prescribe a pseudo-Newtonian vector potential for studying accretion disks
around Kerr black holes. The potential is useful to study the inner properties
of disk not confined to the equatorial plane where general relativistic effect
is indispensable. Therefore, we incorporate the essential properties of the
metric at the inner radii through the pseudo-Newtonian potential derived from
the general Kerr spacetime. The potential, reproducing most of the salient
features of the general-relativity, is valid for entire regime of Kerr
parameter. It reproduces the last stable circular orbit exactly as that in the
Kerr geometry. It also reproduces last bound orbit and energy at last stable
circular orbit with a maximum error ~7% and ~15% respectively upto an orbital
inclination 30 degree.
