Natural convection of an incompressible fluid flow past an infinite vertical flat plate with constant suction velocity is investigated. In this work, we investigate the effect of Grashof parameter on velocity profiles. Unsteady flow is considered and restricted to laminar domain. The equations governing the flow are discretized and solved iteratively using java for various values of Grashof parameter ranging from 0 to 1. Small values of constant suction velocity and constant magnetic field were chosen (v = 2.5 and m2 = 5.0) respectively. The result obtained are then analysed using tables and graphs. The effect of increase of Grashof parameters was addressed. An increase in Grashof parameter leads to an increase in velocity profile near the plate but as the distance from the plate increase the velocity profile decreases.