The Musashi RNA-binding proteins (RBPs) regulate translation of target mRNAs and maintenance of cell stemness and tumorigenesis. Musashi-1 (MSI1), long considered as an intestinal and neural stem cell marker, has been more recently found to be over expressed in many cancers. It has served as an important drug target for treating acute myeloid leukemia and solid tumors such as ovarian, colorectal and bladder cancer. One of the reported binding targets of MSI1 is Numb, a negative regulator of the Notch signaling. However, the dynamic mechanism of Numb RNA binding to MSI1 remains unknown, largely hindering effective drug design targeting this critical interaction. Here, we have performed extensive all-atom microsecond-timescale simulations using a robust Gaussian accelerated molecular dynamics (GaMD) method, which successfully captured multiple times of spontaneous and highly accurate binding of the Numb RNA from bulk solvent to the MSI1 protein target site. GaMD simulations revealed that Numb RNA binding to MSI1 involved largely induced fit in both the RNA and protein. The simulations also identified important low-energy intermediate conformational states during RNA binding, in which Numb interacted mainly with the β2-β3 loop and C terminus of MSI1. The mechanistic understanding of RNA binding obtained from our GaMD simulations is expected to facilitate rational structure-based drug design targeting MSI1 and other RBPs.