In this paper, a new multiscale phase field method (MsPFM) has been proposed to simulate crack propagation in composites. The MsPFM inherits the merits of anisotropic phase field method and multiscale finite element method. It is known that phase field simulation requires dense meshing to represent a sharp crack, thus the main aim of the MsPFM is to achieve mesh refinement in the vicinity of diffused crack/cracks. The proposed method is also used to study the interaction of a pre-existing crack with weak or strong interfaces (between matrix-fibre or between laminates) in terms of crack arrest, crack deflection, crack coalescence, and multiple cracks initiation in composites. Various numerical experiments are performed to demonstrate the effectiveness of proposed MsPFM to simulate the aforementioned failure characteristics of the composites. The crack growth trajectory obtained by the MsPFM for few test cases is validated through standard extended finite element method.