With the help of the static replica symmetric spin glass theory, thermodynamic properties of the Sherrington-Kirkpatrick (SK) spin glass model with the random Dzyaloshinskii-Moriya (DM) interaction in external magnetic fields are investigated. The dependences of entropy, specific heat, susceptibility and the corresponding order parameters on temperature are studied numerically for different magnetic fields and spin numbers 1/2 and 1. It is found that the local susceptibility is in good agreemeat with that given by the thermo-field dynamic theory. Especially, the crossover behavior of the specific heat-temperature curves for different magnetic fields observed by Brodale et al. can be explained very excellently.