Random speckles are proposed to demodulate Fabry-Perot (FP) sensors in this study. A piece of multimode fiber is used to interrogate the FP transmission spectrum, and tiny spectral changes lead to significant variations in the generated speckle patterns. In the demonstration experiments, the pressure resolution of 0.001 MPa can be obtained from an open cavity FP sensor based on the convolutional neural network (CNN) demodulation algorithm. It is worth noting that the spectral differences in neighboring orders can be precisely distinguished due to the high sensitivity of speckles. Thus, the fringe-order ambiguity problem is solved and the dynamic measurement range can be greatly improved. The speckle-based demodulation scheme provides a new way to balance resolution, dynamic range, speed, and cost of FP sensors.