Existing recommendation methods suffer from the data sparsity problem which means that most of users have rated only a very small number of items, often resulting in low recommendation accuracy. In addition, for cold start users evaluating only few items, rating predictions with the methods also produce low accuracy. To address these problems, we propose a novel data imputation method that effectively substitutes missing ratings with probable values (i.e., imputed values). Our method successfully improves accuracy of recommendation methods from the following three aspects: (1) exploiting a trust network, (2) imputing only a part of missing ratings, and (3) applying them to any recommendation methods. Our method employs a bidirectional connection structure within a distance level for finding reliable users in exploiting a trust network as useful information. In addition, our method imputes only some missing ratings, called fillable ratings, whose imputed values are expected to be accurate with a sufficient level of confidence. Moreover, our imputation method is independent of, thus applicable to, any recommendation methods that may include application-specific ones and the most accurate one in each domain. We conduct experiments on three real-life datasets which arise from Epinions and Ciao. Our experimental results demonstrate that our method has recommendation accuracy better than existing recommendation methods equipped with imputation methods or trust networks, especially for cold start users.