Shannon / Nyquist sampling theorem indicates that during the sampling process the minimum sample rate must be more than the double of the band of the signal so that we can achieve images without distortion. High-frequency sampling leads to mass data and results in high cost of storage and transmission procedure. Compressed sensing indicates that we can sample data at far below the Nyquist frequency when the signals are sparse or can be represented as sparse on some orthogonal basis, and the signals can be recovered without distortion after some certain recovery algorithms. By this means the cost of storage and transmission can be reduced significantly. Unlike conventional optical imaging process, this paper presents a new imaging method using a Fourier transform lens system, which enables single-exposure and single-aperture compressed imaging. First, the Fourier transformation of image signals is accomplished after they pass through a Fourier transform optical system. Second, sparse sample data can be obtained after the spectrum signals pass the sensor array. The process mentioned above can be interpreted as that using a Fourier matrix and a sparse matrix to complete the measurement of the image signals. Third, we make use of fast iterative threshold recovery algorithm to compute the sampling values and obtain the target image signals. Compared with the conventional imaging methods, in the case of ensuring the image quality, our method can significantly reduce the number of samples, thus greatly reduce the data redundancy. Simulation results indicate that the imaging method proposed can be prospective.