Compressed Sensing (CS) theory simultaneously realizes the signal sampling and compression process, and can use fewer observations to achieve accurate signal recovery, providing a solution for better and faster transmission of massive data. In this paper, a ternary sampling matrix-based method with attention mechanism is proposed with the purpose to solve the problem that the CS sampling matrices in most cases are random matrices, which are irrelative to the sampled signal and need a large storage space. The proposed method consists of three components, i.e., ternary sampling, initial reconstruction and deep reconstruction, with the emphasis on the ternary sampling. The main idea of the ternary method (-1, 0, +1) is to introduce the attention mechanism to evaluate the importance of parameters at the sampling layer after the sampling matrix is binarized (-1, +1), followed by pruning weight of parameters, whose importance is below a predefined threshold, to achieve ternarization. Furthermore, a compressed sensing algorithm especially for image reconstruction is implemented, on the basis of the ternary sampling matrix, which is called ATP-Net, i.e., Attention-based ternary projection network. Experimental results show that the quality of image reconstruction by means of ATP-Net maintains a satisfactory level with the employment of the ternary sampling matrix, i.e., the average PSNR on Set11 is 30.4 when the sampling rate is 0.25, approximately 6% improvement compared with that of DR2-Net.