We develop a computational model, based on the phase-field method, for cell morphodynamics and apply it to fish keratocytes. Our model incorporates the membrane bending force and the surface tension and enforces a constant area. Furthermore, it implements a cross-linked actin filament field and an actin bundle field that are responsible for the protrusion and retraction forces, respectively. We show that our model predicts steady state cell shapes with a wide range of aspect ratios, depending on system parameters. Furthermore, we find that the dependence of the cell speed on this aspect ratio matches experimentally observed data.