The problem of FIR filtering with noisy input and output data can be solved by a total least squares (TLS) estimation. The performance of the TLS estimation is very sensitive to the ratio between the variances of the input and output noises. In this paper, we propose an iterative convex combination algorithm between TLS and least squares (LS). We combine two typical iterative algorithms, the total least mean square method (TLMS) and the least mean square method (LMS). TLMS is a typical iterative algorithm for TLS and LMS is a typical one for LS. This combined algorithm shows robustness against the noise variance ratio. Consequently, the practical workability of the TLS method with noisy data has been significantly broadened.