A theoretical analysis of two-dimensional, steady state, laminar film condensation on a finite-size horizontal plate facing upward with constant surface heat flux is studied. While the most of previous theoretical studies on the him-wise condensation problem made the assumption of isothermal surface, the present work assumes the condition of constant surface heat flux. Besides, the critical him thickness at the edge of the plate is determined by employing the principle of minimum mechanical energy instead of the method of ＇trial and error＇ or arbitrary assumption used by the most of previous studies. And the dimensionless heat transfer coefficient and the film thickness along the plate are simply expressed in terms of general used parameters Prandtl number (Pr), Reynolds number (Re), and Rayleigh number (Ra).