Lead halide perovskites have demonstrated outstanding performance in photovoltaics, photodetectors, radiation detectors and light-emitting diodes. However, the electromechanical properties, which are the main application of inorganic perovskites, have rarely been explored for lead halide perovskites. Here, we report the discovery of a large electrostrictive response in methylammonium lead triiodide (MAPbI3) single crystals. Under an electric field of 3.7 V µm-1, MAPbI3 shows a large compressive strain of 1%, corresponding to a mechanical energy density of 0.74 J cm-3, comparable to that of human muscles. The influences of piezoelectricity, thermal expansion, intrinsic electrostrictive effect, Maxwell stress, ferroelectricity, local polar fluctuation and methylammonium cation ordering on this electromechanical response are excluded. We speculate, using density functional theory, that electrostriction of MAPbI3 probably originates from lattice deformation due to formation of additional defects under applied bias. The discovery of large electrostriction in lead iodide perovskites may lead to new potential applications in actuators, sonar and micro-electromechanical systems and aid the understanding of other field-dependent material properties.