The paper deals with offset free reference tracking problem for reference signals composed of step and ramp functions. The proposed solution arises from usual design of generalized predictive control supplemented with specific modifications suppressing or ideally removing undesirable offset (steady state error) from required behavior. Furthermore, the modifications may improve additionally the behavior of the control process. The solution follows the usual form of the state-space formulation for multi-input multi-output systems and does not change mathematical model describing the controlled system against other solutions. In that context, the dimensionality of the design stays the same as in case of usual predictive control design. The proposed solution is demonstrated by a simulation of simple single-input single-output system of second order, but developed algorithms are general even for multidimensional systems.