An apparatus of rapid-positioning with curved light surface includes a transmitter and a receiver. The transmitter can emit an optical signal to the receiver. The receiver can receive an optical signal emitted by the transmitter. The apparatus of rapid-positioning with curved light surface determines a position of the receiver according to the optical signal received by the receiver. The transmitter includes: a light emitter capable of emitting optical signals of at least two flicker frequencies; and a hollow hemispherical cover provided with fixed-angle opaque sections and variable-angle opaque sections, and regions between the fixed-angle opaque sections and the variable-angle opaque sections being light transmission regions. Therefore, the apparatus and method of rapid-positioning with curved light surface provided by the present application can accurately position the receiver, and the receiver can be placed on an object surface to receive the optical signal of the transmitter, so as to perform an accurate indoor positioning. Therefore, in an intelligent production environment, a robot can accurately assist to assemble and convey materials and products. The apparatus of rapid-positioning with curved light surface of the present application can perform multiple positioning during one rotation, which can make the positioning faster.