The behavior of cumulus convection in a prevailing wind with vertical shear is studied by integrating a set of dynamic equations numerically. The motion is considered under the solenoidal condition in a vertical two dimensional plane. Aside from the eddy exchange, the pseudo-adiabatic process is assumed in which the motion is moist adiabatic in saturated ascending air and dry adiabatic in the remaining air. The comparison between both cases, with and without vertical shear, is made concerning the time dependent evolution of convections and their energy conversion. In a prevailing wind field with vertical shear, the axial symmetry of the convection is destroyed and the axis of the convection cell tilts downwind with height. This results in the interaction between the convective motion and the prevailing wind which transforms the kinetic energy of the convection into that of the prevailing wind. Therefore, vertical wind shear tends to suppress the development of the convection in the vertical plane parallel to the wind. Moreover, the discrepancy which develops between the central axes of updraft and the warm regions of the convection decreases the conversion of potential to kinetic energyone which contributes to the development of the convection.