A double-clad Yb-doped mode-locked fiber laser that can operate in burst-mode and square-pulse states is experimentally investigated. In the burst-mode state, a burst train with 55 pulses of 500 ps duration is obtained. In the square-pulse state, which is similar to noiselike pulses, the maximum pulse energy is 820 nJ and the duration can be tuned from 15.8 to 546 ns. The square pulses have a narrow and multipeak spectrum, which is quite different from that of normal noiselike pulses. The fiber laser promises an alternative formation mechanism for burst-mode and square-pulse mode-locked fiber lasers.