This paper proposes an adaptively secure solution to certificateless distributed key encapsulation mechanism from pairings by using Canetti\'s adaptive secure key generation scheme based on discrete logarithm. The proposed scheme can withstand adaptive attackers that can choose players for corruption at any time during the run of the protocol, and this kind of attack is powerful and realistic. In contrast, all previously presented threshold certificateless public key cryptosystems are proven secure against the more idealized static adversaries only. They choose and fix the subset of target players before running the protocol. We also prove security of this scheme in the random oracle model.