A hybrid heuristic attack scheme that combines the hill climbing algorithm and the simulated annealing algorithm is proposed to speed up the search procedure and to obtain a more accurate solution to the original key in the Fourier plane encryption algorithm. And a unit cycle is adopted to analyze the value space of the random phase. The experimental result shows that our scheme can obtain more accurate solution to the key that can achieve better decryption result both for the selected encrypted image and another unseen ciphertext image. The searching time is significantly reduced while without any exceptional case in searching procedure. For an image of 64x64 pixels, our algorithm costs a comparatively short computing time, about 1 minute, can retrieve the approximated key with the normalized root mean squared error 0.1, therefore, our scheme makes the known-plaintext attack on the Fourier plane image encryption more practical, stable, and effective.