A physics-based regression algorithm was developed and applied to the Infrared Atmospheric Sounding Interferometer (IASI) observations to estimate atmospheric temperature and humidity profiles. The proposed algorithm utilized three steps to solve the ill-posed problems and to stabilize the solution in a fast speed regression manner: 1) a set of optimal channels was selected to decrease the effect of forward model errors or uncertainties of trace gases; 2) the principal component analysis technique was used to reduce the number of unknowns; 3) a ridge regression procedure was introduced to improve the ill-conditioned problem and to lessen the influence of correlation. To determine the optimal coefficients of the algorithm, a simulated dataset was generated with the spectral emissivities and atmospheric profiles fully covering all the possible situations for clear sky conditions. Then, the accuracy of the algorithm was evaluated against with both simulated and actual IASI data. The root mean squared error (RMSE) of atmospheric temperature profile for the simulated data is about 1.5 K in troposphere and stratosphere and is close to 4 K near the surface with no biases. The RMSE of atmospheric humidity profile for the simulated data is about 0.001-0.003 g/g at low altitude. Although the retrieval accuracy for the actual IASI data is not as good as those for the simulated data, the vertical distribution of atmospheric profiles can be well captured. Those results showed that the proposed algorithm is promising when the profile bias errors could be removed.