A control apparatus for a fuel cell and a fuel cell vehicle is provided capable of controlling a fuel cell installed on a vehicle in an optimized condition. An ECU calculates a target generation current to be output by a current controller from the generation current of the fuel cell, based on a signal of an accelerator opening AC detected by the accelerator opening sensor and a signal of an atmospheric pressure detected by the atmospheric pressure sensor, and the target generation current is input into the current controller as the current command value. The current controller controls the generation current to be output from the fuel cell based on the current command value output from the ECU, that is, the generation command to the fuel cell.