A new method for two dimensional damped sinusoids estimation in colored Gaussian noise, called two dimensional fourth order mixed cumulants based on ESPRIT (2d FOMCESPRIT), is presented. The amount of computations is greatly reduced by holding the dimensions of the feature matrix compared with that of the former methods in the presence of a long record. Due to FOMC's auto suppressing Gaussian noise, the SNR threshold is reduced and the precision of the parameter estimation is improved. Simulation results show that this method is of better performance and higher efficiency than the former methods in colored Gaussian noise.