The detection of the state of polarization (SOP) of light is essential for many optical applications. However, cost-effective SOP measurement is a challenge due to the complexity of conventional methods and the poor transferability of new methods. We propose a straightforward, low-cost, and portable SOP measurement system based on the multimode fiber speckle. A convolutional neural network is utilized to establish the mapping relationship between speckle and Stokes parameters. The lowest root-mean-square error of the estimated SOP on the Poincaré sphere can be 0.0042. This method is distinguished by its low cost, clear structure, and applicability to different wavelengths with high precision. The proposed method is of great value in polarization-related applications.