Different from standard sampling strategy in compressive sensing (CS), we present a compressive partial sampling framework called adaptive-random sampling and recovery (ASR) for image. It could faithfully recover images by hybridizing random samples with edge-extracted pixels with much lower sampling rate. The new framework preserves edge pixels containing essential information of images, and meanwhile employs the edge-preserving total variation (TV) regularizer. Assisted with the edges, three steps are adopted to recover the high-quality image. First, we extract the edges of a coarse image recovered with completely random measurements in our sampling framework. Then, the TV algorithm in the CS theory is employed for solving the Lagrangian regularization problem. Finally, we refine the coarse image to obtain a high-quality one with both the extracted edges and previous random measurements. Experimental results show that the novel ASR strategy achieves significant performance improvements over the current state-of-the-art schemes.