The problem of stainless steel brazing is still the focus of scientific research. In this work, the Mn-based brazing filler was used to braze 1Cr18Ni9Ti and 1Cr21Ni5Ti stainless steel. The typical microstructure of the 1Cr18Ni9Ti/1Cr21Ni5Ti joint was analyzed in detail, and the interface structure of the joint was determined to be 1Cr18Ni9Ti/Mn(s, s)/1Cr21Ni5Ti. The brazing temperature and holding time were shown to have a great influence on the microstructure of the brazed joint. The tensile strength of brazed joints first increased and then decreased with the rising of the brazing temperature and the holding time. The maximum tensile strength was 566 MPa when the joints were brazed at 1125 °C for 15 min. The diffusion of Mn and Cr was an important factor affecting the quality of the joints. The diffusion distances of Mn and Cr at different brazing temperatures and holding times were measured, and the diffusion activation energy and diffusion coefficient were achieved by the Arrhenius equation.