The strengths of the vibration—rotation lines of the first overtone, first hot band, and fundamental band of HBr have been measured by a curve of growth method, applying a correction for two overlapping lines devised by Sakai. The squares of the electric-dipole matrix elements |M02(m) |2 and |M12(m) |2 for the lines have been calculated, and have been fitted, respectively, to a cubic and quadratic polynomial in m, using the method of least squares. The experimental results for all three bands are compared with the theory of Herman and Wallis. The fact that the experimental |M02(0) |2 is less than that calculated from a linear dipole-moment function clearly requires a positive value of M2, the second derivative of the dipole-moment function. The squares of the matrix elements |M01(0) |2 and |M02(0) |2 are used to calculate M1 and M2, the dipole-moment coefficients, for Morse and anharmonic oscillators. Of all the possible sets of M1 and M2 obtained in each case, the one giving results in better agreement with |M12(0) |2 is chosen. The chosen values of the dipole-moment coefficients are M1=+4.56×10−11 esu and M2=+0.69×10−3 esu cm−1 for the Morse oscillator and M1=+4.63×10−11 esu and M2=−0.70×10−3 esu cm−1 for the anharmonic oscillator. Since the sign of M2 is positive, the Morse oscillator results are preferred.