This paper analyzes the effect of heat source and variable magnetic field on unsteady hydromagnetic viscous stratified flow past a moving porous flat plate under slip boundary condition for velocity field and jump in temperature field. The velocity of the porous plate decreases exponentially with time about a constant mean and a variable suction velocity is applied normal to the plate. A variable magnetic field is applied in the transverse direction in the form �for �The governing equations of the flow field are solved employing perturbation technique and the expressions for velocity field, temperature distribution, skin-friction and the heat flux in terms of Nusselt number are obtained. The effects of the pertinent parameters on the velocity and temperature distribution of the flow field are analyzed and discussed with the aid of figures and tables. It is observed that the effect of growing magnetic parameter (M) / velocity slip parameter �is to retard the velocity, while the stratification parameter (a) enhances the magnitude of the velocity and temperature of the flow field at all points and reduces the magnitude of both skin friction and heat flux at the wall. The suction velocity parameter (A) decreases the magnitude of the velocity of the flow field near the plate and thereafter the flow behaviour reverses. A growing Prandtl number (Pr)/ heat source parameter (S ) enhances the temperature at all points of the flow field and the temperature jump parameter / magnetic parameter (M ) shows the reverse effect.