A gradient-based steering kernel (GradSK) reconstruction strategy for compressed remote sensing is proposed. It aims to solve the artifacts and blurriness caused by the none-strictly sparsity and the noisy Fourier undersamples. Semi-random Fourier measurements are presented for encoding, which can preserve approximating components of images and retain the incoherence by random undersamples in the periphery of K-space. The steering kernel derived from multistep gradients is exploited to encapsulate with finite-difference Total Variance (TV) in the unconstrained convex framework for decoding. Numerical results demonstrate the superior performance of this algorithm in the case of noiseless and noisy measurements for compressed remote sensing.