Multiple signal classification (MUSIC) time delay estimation is a classical and effective super-resolution method for the wideband signal. However, when the transmitted signal becomes narrowband, the resolving power of this algorithm degrades severely, and if the transmitted signal is continuous wave (CW), the algorithm does not work at all. As the noise subspace of time delay correlation matrix will be contaminated by signal in narrowband scenario, MUSIC is unable to distinguish the closely arrived echoes. In this study, a novel algorithm, named as diagonal loading least squares MUSIC (DL-LS-MUSIC), is proposed to solve the problem. The correlation matrix is reconstructed by the channel response which is estimated by DL-LS. With a pre-processing procedure, MUSIC time delay estimation becomes robust and it is proved by simulation. Furthermore, the pool experiment indicates the novel algorithm can estimate time delays more accurately than the original MUSIC especially for CW signals.