In this study, the adaptive triangular beam method(ATBM) considering different sound reflection coefficients and angles of a triangular beam on two or more planes as well as diffraction effect is suggested. The ATBM, subdividing a tracing triangular beam into multiple triangular beams on reflection planes, gives reliable and convergent sound-field analysis results without the dependancy on the number of initial triangular beam segmentation to search sound propagation paths from source to receiver. The validity of the method is verified by the comparison of numerical and experimental results for energy decay curve and steady-state sound pressure level of rooms having direct, reflective and diffractive sound paths.