A power converter for a fuel cell is provided. The power converter includes a boost converter connected to the fuel cell and configured to control a load voltage at a predetermined magnitude in a normal operation mode and to induce an output response by applying a predetermined perturbation current to the fuel cell in a diagnosis mode, and a digital signal processor configured to extract an impedance parameter by detecting the output response of the fuel cell in the diagnosis mode, and predict a lifespan of the fuel cell according to the impedance parameter. The normal operation mode is configured to supply a voltage in response to a change of a load and the diagnosis mode is configured to predict the lifespan of the fuel cell.