Tracking of a time-varying channel is a challenging task, especially when channel is non-stationary. In this work, we propose a time-varying q-LMS algorithm to efficiently track a random-walk channel. To do so, we first perform tracking analysis of the q-LMS algorithm in a non-stationary environment and then derive the expressions for the transient and steady-state tracking excess mean-square-error (EMSE). Thus, we evaluate an optimum value of q parameter which minimizes the tracking EMSE. Next, by utilizing the derived optimum q, we design a time-varying mechanism to vary the parameter q according to the estimation of instantaneous error energy which provides faster convergence in the initial phase while attain a lower EMSE near final stages of adaptation.