We propose a new Grid-based SLAM method with partial map matching for considering previous sensor data in Rao-Blackwellized Particle Filter. The partial maps are built probabilistically as accumulated scan shapes for each particle. In conventional Grid-based SLAM methods, Rao-Blackwellized Particle Filter is often used. However, the conventional methods sometimes fall into misalignment and fail to build proper maps in large or limited visibility environments. In those environments, the sensor data becomes insufficient shape to match with maps for localization since the sensor field of view is limited. It causes misalignment and failure in localization and map building. Rao-Blackwellized Particle Filter of the conventional methods is based on a Hidden Markov Model that uses only current sensor data to estimate robot poses. Hence, if the current sensor data is insufficient, it is difficult to estimate robot poses and build maps correctly. In our new method, the Hidden Markov Model has been extended to utilize a series of sensor data from the past in several seconds to the present. The series of sensor data is accumulated to make scan shape sufficient for the matching in localization. Thus, the proposed method is expected to cover the lack of sensor field of view by means of the accumulation of sensor data, and is capable of mapping in large or limited visibility environments. In our experiments at Tsukuba Challenge 2014 and Tsudanuma Campus, consistent maps were built only by the proposed method. Shape errors of the maps built by the proposed method were smaller than the conventional method.