In the case of ordinary identification coding, a code is devised to identify a single object among N objects. But, in this paper, we consider a coding problem to identify K objects at once among N objects in the both cases that K objects are ranked or not ranked. By combining Moulin-Koetter scheme with the ε-almost strongly universal class of hash functions used in Kurosawa-Yoshida scheme, an efficient and explicit coding scheme is proposed for K-multiple-object identification (K-MOID) coding. Furthermore, it is shown that the K-MOID capacity CK-MOID, which is the maximum achievable coding rate in the K-MOID coding, is equal to the ordinary channel capacity, and the proposed scheme can attain CK-MOID.