Improving Salpeters method, we discuss the effect of superstrong magnetic fields (such as those of magnetars) on thermonuclear reaction rates. These most interesting reactions, including the hydrogen buing by the CNO cycle and the helium buing by the triple alpha reaction, are investigated as examples on the magnetar surfaces. The obtained result shows that the superstrong magnetic fields can increase the thermonuclear reaction rates by many orders of magnitude. The enhancement may have significant influence for further study research of the magnetars, especially for the x-ray luminosity observation and the evolution of magnetars.