Convection is the convective heat transfer from one place to another place which is caused by the movement of
fluid. Analytical solution of the convection equation is developed from nonlinear of Navier-Stokes. This paper considers the steady boundary layer flow and heat transfer of viscoelastic fluid past an elliptic cylinder. The heat transfer comes from the surface is proportional to the both of temperature on surrounding cylinder surface and the velocity of the fluid. The governing equations are developed from continuity, momentum, and energy conservation. Further, those equations are transformed into boundary layer equations. The boundary equations further are transformed into nondimensional form. The similarity equations is applied to solve the non-dimensional form easily. We further solve the equations numerically by using the finite difference method. The numerical results show that the temperature and the velocity distributions decrease when the Prandtl number increases. For the variation of the viscosity variable, the temperature distributions increase and the velocity distributions decrease when the viscosity variable increases.