We investigated the stability of cryocooler-cooled high-temperature superconducting (HTS) coils by using a computer program based on FEM. In this study, the current at which "thermal runaway" occurs, which depends on the relationship between the cooling power of the cryocooler and the heat generation in HTS coils, was adopted as a stability criterion of cryocooler operating HTS coils. It was shown that cryocooler-cooled HTS coil was stable in operating current above the critical current from the numerical analysis results by HTS model coil. And also, if we efficiently remove the heat generation from HTS coils by potimizing heat drain, the ramp-rate limitation can be mitigated because the effect of AC loss by the current rise was too small. Furthermore, in the case of pulsed operation; the HTS model coil is ramped from zero to the peak value in one second and back to zero current in one second, such as the operation of SMES device, the peak value of poerating current is 1.5-2 times greater than that of the thermal runaway current.