The invention provides an underground curved roadway tunneling construction method. The method comprises the steps of utilizing computer mapping software to draw a curved roadway vertical view, measuring the center chord length and the circle center angle corresponding to the center chord, mapping out the number of construction tunneling steps, calculating and obtaining the tunneling step length,the tunneling step angle and the tunneling width, and excavating and obtaining a curved roadway according to the geometric parameters of the construction tunneling steps. By the adoption of the technical scheme, the computer mapping software is utilized as a tool, constructors can intuitively learn the situation preliminarily before excavation, then the curved roadway vertical view is divided intoa plurality of construction tunneling steps, a computer is utilized for directly calculating and obtaining the tunneling width, the tunneling length and the tunneling step angle needing to be excavated in each construction tunneling step, the constructors carry out accurate construction, the construction quality is ensured, and the excavation deviation between the curved roadway formed after construction and a curved roadway in the original design paper is reduced.