A longitudinal and lateral vehicle motion cooperative control method based on a fast solving algorithm comprises the following steps: calculating a desired yaw rate according to a steering wheel rotation angle and a current vehicle traveling speed; constructing a nonlinear optimization problem according to the desired yaw rate and a current actual motion state of a vehicle, wherein an objective function of the nonlinear optimization problem is used for tracking the desired yaw rate, and simultaneously for restraining a lateral speed and a tire slip ratio of the vehicle; solving the nonlinear optimization problem to calculate desired slip ratios of four tires; calculating an additional torque of each tire according to an actual slip ratio and the desired slip ratio of the tire; and sending the additional torque of each tire to an actuator of the vehicle for cooperative control.