This paper presents a novel electrochemical machining process for machining microstructure arrays on curved surfaces of parts. A set of electrolytic systems with the rolling device was constructed to machine micro-pit arrays on various metal part surfaces. Numerical simulations were conducted to investigate the electric field distribution characteristics and their spatial evolution over time, as well as the geometric profile evolution of the forming microstructures. Experimental tests were carried out on the surface of a 304 stainless steel workpiece using a 10% NaNO3 electrolyte and a 0.1 mm electrode gap. The effects of voltage, the rotating speed of the roller and the linear cathode size on the morphology of micro-pit arrays were explored. The results showed that micro-pit arrays could be successfully machined on the plane, outside and inside surface of the workpiece. Under the 10.5 V applied voltage and 0.2 r/min rotating speed of the workpiece, the diameter of the micro-pit was 421.55±18.75 μm, the depth was 70.2±4 μm, the average etch factor(EF) was 1.16, and the roughness of the micro-pit was 0.625±0.205 μm. This work provides a promising strategy for high-precision batch machining micro-pit arrays on the plane and curved surfaces of the workpiece.