In this paper, we consider a phase-field model for dendritic growth in a two-dimensional cavity flow and propose a computationally efficient numerical method for solving the model. The crystal is fixed in the space and cannot be convected in most of the previous studies, instead the supercooled melt flows around the crystal, which is hard to be realized in the real world experimental setting. Applying advection to the crystal equation, we have problems such as deformation of crystal shape and ambiguity of the crystal orientation for the anisotropy. To resolve these difficulties, we present a phase-field method by using a moving overset grid for the dendritic growth in a cavity flow. Numerical results show that the proposed method can predict the crystal growth under flow.