This work describes a phase-resolving wave forecasting algorithm that is based on the assimilation of marine radar image time series. The algorithm is tested against synthetic data and field observations. As developed, the algorithm couples X-band marine radar observations with a phase-resolving wave model that uses the linear Mild Slope Equations (MSEs) for reconstruction of water surface elevations over a large domain and a prescribed time window. The reconstruction also enables wave-by-wave forecasting through forward propagation in space and time. Marine radar image time series provide the input wave observations through a previously given relationship between backscatter intensity and the radial component of the sea surface slope. The algorithm assimilates the wave slope information into the model via a best-fit wave source function at the boundary that minimizes the slope reconstruction error over an annular region at the outer ranges of the radar images. The wave model is then able to propagate the waves across a polar domain to a location of interest at nearer ranges. The constraints on the method for achieving real-time forecasting are identified and the algorithm is verified against synthetic data and is tested using field observations.