It is well known that for non-monotonic profiles of the safety factor q with two q = m/n resonant surfaces inside the plasma (m/n being the poloidal/toroidal mode numbers), the low-m double tearing modes (DTMs) are usually unstable, especially for plasmas with a high bootstrap current fraction as required for the steady operation of advanced scenarios. The effect of applied resonant magnetic perturbations (RMPs) on the m/n = 2/1 DTM growth is investigated numerically in this paper using two-fluid equations. The DTM growth is found to be stabilized by moderate static m/n = 2/1, 4/2 or 6/3 RMPs below their penetration threshold if the distance between the two resonant surfaces and the local plasma rotation velocity at the outer resonant surface are sufficiently large. The outer magnetic island is stabilized due to the change of the local plasma current density gradient around the outer resonant surface caused by RMPs, while the inner island growth is stabilized by the bootstrap current perturbation in the negative magnetic shear region. The mode stabilization is more effective for a higher electron temperature, indicating a possible method to improve the DTM stability in a fusion reactor.