A single-longitudinal-mode 1521 nm pulse microchip laser Q-switched by a Co2+:MgAl2O4 saturable absorber was demonstrated in an Er:Yb:YAl3(BO3)4 crystal. The influence of the waist radius of pump beam at 976 nm on the laser performance was investigated. At an incident pump power of 6.54 W and pump beam waist radius of 60 μm, a 1521.4 nm single-longitudinal-mode pulse laser with average output power of 434 mW, energy of 16.5 μJ, repetition frequency of 26.3 kHz and width of 2.9 ns was obtained. The result shows that caused by the mode selection of the saturable absorber and large cavity losses, a single-longitudinal-mode 1.55 μm pulse microchip laser can also be realized in the Er:Yb:YAl3(BO3)4 crystal.