The generation of laser driven plasma wake wave has been investigated in hydrogen pair-ion electron plasma. The consideration of dynamics of the positive and negative ion pair have been adopted. Inclusion of the ion motion has the effect of modifying the electric field and density profiles of the wake wave. This has been demonstrated by observing the variation of the electron density and electric field profiles with the change in positive ion/negative ion concentration. High density spikes and sawtooth like electric field profiles (indication of wave breaking) are observed to transform into sinusoidal electric field profile and low amplitude density profile when the positive ion density in the plasma system is kept higher. Furthermore, we observe the variation of the electric field amplitude of the wake wave with the laser pulse width. This feature is the indication of the possibility of hybrid acceleration (Direct Laser Acceleration and wake field acceleration) of accelerated beam. The results are quite relevant in laser plasma interaction field in experimental physics and also in planetary environment.