The basic structure of Variable Curvature Friction Pendulum Isolation Bearing (VCFP) is introduced. Based on the principle of mechanical equilibrium, theoretical analysis on two types of VCFP which are Variable Frequency Pendulum Isolation Bearing (VFPI) and Conical Friction Pendulum Bearing (CFPI) are conducted. The stiffness of each VCFP is derived, and the recovery characteristics were discussed and the computing formula of maximum residual displacement was deduced as well. Moreover, with the use of ABAQUS software, the models with solid element of each VCFP are built, and the hysteresis property under low cyclic loading and recovery characteristic are simulated. The comparative analysis of VCFP and Friction Pendulum Bearing (FPB) are also conducted. The results show that: 1) the numerical simulation results are identical to the theoretical analysis; 2) according to its plump hysteresis loops, the hysteresis property of VCFP is favorable, further more, its effective viscous damping ratio and coefficient of energy dissipation are higher than FPB, which indicates its greater ability in energy dissipation; 3) the stiffness of the VCFP is determined by curvature radius, that is, sliding surface function. And its stiffness decreases with the increase of bearing displacement through rational design. And then its isolation period increases as the displacement increases and the low frequency resonance problem of isolated structures can be well solved; 4) compared with FPB, the softening mechanism of stiffness can make the shear force transferred to superstructure decrease; 5) the maximum stress of bearing appears when the bearing reaches its designed displacement, and in general it may situate in the edge of ball joint surface of slider or bearing plate 6) the maximum residual displacement of VCFP depends on both friction coefficient and the parameters of sliding surface function, therefore, parametric design based on analysis or simulation is necessary so as to control the maximum value in an acceptable range in engineering.