Conventional GPS acquisition methods, such as Max selection and threshold crossing (MAX/TC), estimate GPS code/Doppler by its correlation peak. Different from MAX/TC, a multi-layer binarized convolution neural network (BCNN) is proposed to recognize the GPS acquisition correlation envelope in this article. The proposed method is a double dwell acquisition in which a short integration is adopted in the first dwell and a long integration is applied in the second one. To reduce the search space for parameters, BCNN detects the possible envelope which contains the auto-correlation peak in the first dwell to compress the initial search space to 1/1023. Although there is a long integration in the second dwell, the acquisition computation overhead is still low due to the compressed search space. Comprehensively, the total computation overhead of the proposed method is only 1/5 of conventional ones. Experiments show that the proposed double dwell/correlation envelope identification (DD/CEI) neural network achieves 2 dB improvement when compared with the MAX/TC under the same specification.