This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers for discrete-time Linear Parameter-Varying (LPV) systems. In practical systems, it can be hardly expected that exact scheduling parameters are available, it is therefore supposed that inexact scheduling parameters with bounded uncertainties are provided to GSOF controllers. The bounded uncertainties can contain absolute uncertainties as well as proportional uncertainties simultaneously; that is, our problem does not care about the types of the uncertainties as long as the uncertainties are bounded. We propose a design method to solve the problem in terms of parameter-dependent Bilinear Matrix Inequality (BMI) conditions; however while some conservatism is introduced, it can be reduced to parameter-dependent Linear Matrix Inequality (LMI) conditions with a single line search parameter. A numerical example illustrates the effectiveness and possible conservatism of our method.