Solid Oxide Fuel Cells (SOFC) can serve a large variety of both mobile and stationary applications. In comparison with proton exchange membrane fuel cell technology they have higher efficiency and certain other advantages. However if their potential is to be fully exploited, tighter control is needed because of the SOFC sensitivity to high temperature and fuel utilization variations resulting from load changes. This problem is addressed in the paper by using the ability of model predictive control to respect range and rate constraints. Optimum conditions for the SOFC operation are achieved by satisfying a set of temperature, fuel utilization and air utilization constraints. Significant SOFC nonlinearity is accounted for by using MPC based on multiple linear models. The main control objective is to keep the cell output DC voltage constant despite load variations while respecting all constraints. This constant output voltage operation is important in applications, where the load is primarily of DC type or where the power conditioning unit has no voltage controllability. Simulation results confirm good performance of the proposed multi-linear controller.