This paper describes a new magnetic map-matching algorithm structure based on sequential batch fusion. The proposed algorithm enables real-time computation and more stable indoor localization of mobile robots. Conventional magnetic map-matching-based localization has the disadvantage that real-time navigation is not possible when using a batch process, and navigation fails or has significant localization errors owing to similar magnetic field distortion. This study proposes that measurement updates should be performed based on the convergence of weights with several grid points by repeatedly updating the weights of the grid points using magnetic field similarity. The performance of the proposed navigation algorithm was verified using an open dataset, and the proposed technique had a position error of 1 m even in a path in which navigation using the conventional method failed. It provides an indoor mobile robot navigation algorithm that is significantly cheaper than other conventional sensor-based indoor navigation systems.