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We demonstrate the Q-switched and mode-locked pulse generation, using Molybdenum Aluminum Boride (MoAlB) material as a saturable absorber (SA). The SA film was obtained by mixing MoAlB with a polyvinyl alcohol (PVA) solution and then evaporating the mixture on a petri-dish. The prepared MoAlB PVA thin film exhibits a saturable absorption characteristic of 10.4%. Being introduced into an Erbium-doped fiber laser (EDFL) cavity, the MoAlB PVA thin film provides a stable Q-switched pulse at 1559 nm, which is achieved by adjusting the pump power above the threshold equal to 30.2 mW. The pulse has a maximum repetition frequency of 82.92 kHz, a minimum pulse width of 2.14 μm, and a maximum energy of 27.49 nJ at the pump power equal to 83.8 mW. Also we obtain the mode-locked pulse at 1560.1 nm, when the cavity length is extended to 205 m. The repetition frequency, pulse width, and time bandwidth product of the mode-locked pulse are 0.989 MHz, 3.82 ps, and 0.329, respectively. To the best of our knowledge, this is the first time that Q-switched and mode-locked pulses are obtained in a fiber laser based on MoAlB material. [ABSTRACT FROM AUTHOR]