Here we report a novel single-walled carbon nanotube (SWNT) based bimorph electromechanical actuator, which consists of unique as-grown SWNT films as double electrode layers separated by a chitosan electrolyte layer consisting of an ionic liquid. By taking advantage of the special hierarchical structure and the outstanding electrical and mechanical properties of the SWNT film electrodes, our actuators show orders-of-magnitude improvements in many aspects compared to previous ionic electroactive polymer (i-EAP) actuators, including superfast response (19 ms), quite wide available frequency range (dozens to hundreds of Hz), incredible large stress generating rate (1080 MPa/s), and ultrahigh mechanical output power density (244 W/kg). These remarkable achievements together with their facile fabrication, low driving voltage, flexibility, and long durability enable the SWNT-based actuators many applications such as artificial muscles for biomimetic flying insects or robots and flexible deployable reflectors.