Invention of atomic clock dramatically improved accuracy of time measurement, such as time scale, which is an application of atomic clock. However, even the best atomic clock accumulates error, or time deviation, which grows with time. For that reason, compensating for this deviation is a fundamental problem. In this paper, we propose an estimation method using Recursive Least-Squares Method with Vector-type Variable Forgetting Factor (VVFF-RLS) for multiple atomic clocks system. In multiple atomic clocks system, achieving reliable estimation of time deviations of atomic clocks is one of the most important tasks. An atomic clock, which counts the inter-atomic transition frequency to keep an accurate one second, sometimes suffers its abnormal behaviours of frequency due to environmental factors. The proposed method employs vector-type variable forgetting factor whose each component is allocated for the corresponding clock, and achieves a reliable estimation by sequentially determining the forgetting factor on the basis of the frequency stability. The usefulness of the proposed method is validated through numerical examples.