The effect of a uniform cross flow (injection/ suction) on the transient energy growth of a plane Poiseuille flow is investigated. Non-modal linear stability analysis is carried out to determine the two-dimensional optimal perturbations for maximum growth. The linearized Navier-Stockes equations are reduced to a modified Orr Sommerfeld equation that is solved numerically using a Chebychev collocation spectral method. Our study is focused on the response to external excitations and initial conditions by examining the energy growth function G(t) and the pseudo-spectrum. Results show that, the transient energy of the optimal perturbation grows rapidly at short times and decline slowly at long times when the crossflow rate is low or strong. In addition, the maximum energy growth is very pronounced in low injection rate than that of the strong one. For the intermediate crossflow rate, the transient energy growth of the perturbation, is only possible at the long times with a very high-energy gain. Analysis of the pseudo-spectrum show that the nonnormal character of the modified Orr-Sommerfeld operator tends to a high sensitivity of pseudo-spectra structures.