This paper presents an approach to joint tracking for capturing and classification (JTCC). Target tracking for capturing requires that the estimates be within a close neighborhood of the estimand rather than have a small average error, as for traditional tracking problems. Target classification determines the class of targets. Tracking for capturing is an estimation problem while classification is a decision problem, and they are highly coupled. So JTCC is a joint decision and estimation (JDE) problem. To solve this problem jointly, we first consider a generalized Bayes risk in a previously-proposed JDE framework. By minimizing this Bayes risk, we obtain the joint solution, and its estimation part simplifies to a generalized maximum a posteriori estimator. The JTCC approach adequately addresses the coupling between decision and estimation and the specifics of tracking for capturing. To evaluate the proposed algorithm jointly, we also give a joint performance measure: joint capturing and correct classification rate. Simulation results show that JTCC outperforms the decision-then-estimation, the separate decision-and-estimation, and the conditional joint decision-and-MMSE-estimation methods in joint performance measure.