In real applications of data mining, machine learning and granular computing, measurement errors, test costs and misclassification costs often occur. Furthermore, the test cost of a feature is usually variable with the error range, and the variability of the misclassification cost is related to the object considered. Recently, some approaches based on rough sets have been introduced to study the error-based cost-sensitive feature selection problem. However, most of them consider only single-granularity cases, thus are not feasible for the case where the granularity diversity between different features should be taken into account. Motivated by this problem, we propose a multi-granularity feature selection approach which considers measurement errors and variable costs in terms of feature-value granularities. For a given feature, the feature-value granularity is evaluated by the error confidence level of the feature values. In this way, we build a theoretic framework called confidence-level-vector-based neighborhood rough set, and present a so-called heuristic feature-granularity selection algorithm, and a relevant competition strategy which can select both features and their respective feature-value granularities effectively and efficiently. Experiment results show that a satisfactory trade-off among feature dimension reduction, feature-value granularity selection and total cost minimization can be achieved by the proposed approach. This work would provide a new insight into the cost-sensitive feature selection problem from the multi-granularity perspective.