To solve the problem that the detection performance of over the horizon radar (OTHR) is seriously affected by the transient interference, an adaptive transient interference suppression method is proposed based on time-frequency double sparsity (TFDS). The TFDS takes the double sparsity of transient interference in the slow-time domain and sea clutter in the frequency domain as the priori information to construct the objective function. Then, optimizing the objective function by the alternating direction multiplier method (ADMM) to suppress the transient interference. The TFDS can adaptively separate interference and recover pure spectrum with a low computational complexity. Experimental results show that the TFDS has better interference suppression performance and noise robustness than the existing methods.