Muography is a green and non-destructive technology, which is widely applicable in various fields such as geophysical exploration, archaeology, and nuclear safety. This article transforms the muography inversion problem into an optimization problem, and proposes utilizing a first-order optimization algorithm, stochastic gradient descent with momentum (SGDM), to solve it. SGDM is well-suited for such tasks due to its ability to handle large-scale optimization challenges efficiently. To evaluate its effectiveness, two kinds of scenes, single-density anomaly scene and multi-density anomaly scene, are provided. Simulation results show that the distributions and densities of anomalies in prediction images are closely similar to theoretical images, and simulation results of the SGDM method are closer to theoretical results than traditional methods. This highlights the significance of applying SGDM in muography inversion, offering a promising approach to solving complex muography problems.