We study in this paper, a one parameter deformation of the q-Laguerre weight function. An investigation is made on the polynomials orthogonal with respect to such a weight. With the aid of the two compatibility conditions previously obtained in Chen and Ismail (1997) and the q-analog of a sum rule obtained in this paper, we derive expressions for the recurrence coefficients in terms of certain auxiliary quantities, and show that these quantities satisfy a pair of first order non linear difference equations. These difference equations are similar in form to the recognized asymmetric discrete Painleve systems such as α. q-P-IV and α. q-P-V.