Abstract: Based on the hopping characteristics of kangaroos,a spring-mass model of hopping kangaroo robot is deve-loped.The dynamic equation is established using Lagrange method and linear approximation.The radial motion and horizontal motion during stance phase are analysed.According to gait stability conditions,the apex return map function,existence of fixed point and stability of fixed point of hopping kangaroo robot are studied.The range of each parameter which satisfies gait stability during kangaroo robot hopping process and the explicit relational expression of parameters are obtained.Finally,the linear approximation analysis is proved by example to be effective and the relation among parameters when kangaroo robot hops stably is obtained.