This study investigates in laminar falling film condensations over a vertical plate with an accelerating vapor flow conditions. These conditions are considered here in this work by allowing the vapor stream to strike onto the vertical plate surface with an inclination angle. Additional effects are also considered in this work such as presence of liquid suction or slip effects at the cold plate surface. The following assumptions were made: (i) Laminar flow and constant properties are assumed for liquid film. (ii) The gas is assumed to be pure vapor with a uniform saturation temperature. (iii) The shear stress at the liquid interface is negligible. The appropriate fundamental governing partial differential equations for the condensate and vapor flows (continuity, momentum and energy equations) for the above case are identified. Then, they were non-dimensionalized and transformed using non-similarity transformation. The transformed equations were solved using numerical, iterative and implicit finite difference methods. The outcomes of this study show that the vapor strike angle has insignificant influence on the condensation or heat transfer rates, except when slip condition is present and at relatively small values. Moreover, the results also show that increasing the values of the dimensionless suction parameter (Vs) leads to an increase in dimensionless mass of condensate [ ] and Nusselt number [ ]. Thus, it results to increases in condensation and heat transfer rates. Finally, it is found that the condensation and heat transfer rates increase as Grashof number, Jakob number, slip parameter and saturation temperature increase.