In Monte Carlo neutron transport calculations for local response or deep penetration problems, some estimation of an importance function is generally required in order to improve their efficiency. In this work, a new recursive Monte Carlo (RMC) method, which is partly based on the original RMC method, for estimating an importance function for local variance reduction (i.e., source-detector type) problems has been developed. The new RMC method is applied to two sample problems of varying degrees of neutron penetrations, namely, a one-dimensional iron slab problem and a three-dimensional concrete-air problem. Biased Monte Carlo calculations with variance reduction parameters based on the obtained importance functions by the new RMC method are performed to estimate detector responses in these problems. The obtained results are in agreement with those by the reference unbiased Monte Carlo calculations. Furthermore, the biased calculations offer an increase in efficiency on the order of 1 to 104 in terms of the figure of merit. The results also indicate that the efficiency increased as the neutron penetration became deeper.