The heat generation effect on natural convection flow along and conduction inside a vertical flat plate is investigated. The developed governing equations with the associated boundary conditions for this analysis are transferred to dimensionless forms using a local non-similar transformation. The transformed non-linear equations of the non-dimensional equations are then solved using the implicit finite difference method with Keller box-scheme. Numerical results are found for different values of the heat generation parameter, conjugate conduction parameter and Prandtl number. The overall investigation of the velocity, temperature, skin friction and heat transfer rate are presented graphically.