This study presents a means of solving the inverse boundary value problem of coupled heat and moisture transport in an annular cylinder. While knowing the temperature history at any point of the body, the boundary time-varying moisture flux can be computed and subsequently the moisture distribution in the body can be determined as well. The surface moisture flux is then determined to minimize the sum of squares of the deviation between the calculated and measured temperatures in the body. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained on the surface and in an interior location of the cylinder. Numerical results demonstrate that excellent estimations on the moisture distributions can be obtained for all the test cases considered here. The proposed method is highly promising for designing a moisture sensor for some solids.