We have proposed a multi-grid type MSGC (M-MSGC) to overcome the problems of conventional MSGCs. Additional grid strips are inserted between the anode and the cathode in this new type of MSGC. Because the grid strips has lower potentials than the anode, the field strength around the neighboring grid to the anode strip is not as high as the conventional small-gap MSGCs, which assures higher gas gain and safe operation at a high counting rate. We are now developing a charge integrating type M-MSGC for very high counting applications. Because most of the surface of the M-MSGC plate is covered with metal strips, we can expect a very high counting rate detector based on the charge integrating method. This paper describes the first test result on the charge integrating type M-MSGC using X-rays at KEK Photon Factory. The detector system has shown a good linearity more than 10 6 cps/mm 2 .