In the paper we investigate the characteristics of a short-cavity fiber laser based on a new silica fiber with a composite erbium-doped phosphosilicate core without additional co-doping with ytterbium. For the first time, the operation of such laser in the continuous-wave lasing mode with 1490-nm pump is shown. The laser operation in the self-Q-switching mode, changing to the continuous-wave mode with increasing the pumping power, is demonstrated.