In acid fracturing, acid is injected into artificial fracture to dissolve the rock, and the rock surface is shaped into the non-uniform morphology. This non-uniform morphology is the main cause of fracture conductivity after acid etching. The effects of acid type, flow rate, contact time and rock type on the non-uniform morphology of acid-etched rock surface have been studied. However, when the direction of acid flow is determined, the difference of dissolution characteristics in different directions of rock surface is not investigated. In this paper, acid rock reaction experiment and analysis of rock surface morphology after acid etching are carried out by using rock samples with flat surface. The difference of morphological characteristic parameters of rock surface in different directions under the condition of acid flow is discussed. It was found that the mean drop height, drop height range and roughness coefficient increase with the increase of acid rock reaction rate on flat rock surface. The morphological characteristic parameters of acid-etched rock face of limestone are greater than those of dolomite, which is conducive to forming acid-etched channels. According to the statistics of all experimental data, the larger average drop height of rock surface is distributed in the direction of parallel acid flow, the larger drop height range is distributed in the direction of vertical acid flow and other directions, and the larger roughness coefficient is distributed in other directions.