In the classical secret-key generation model, common randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this paper, the secret-key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated secret-key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the secret-key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally, a single-letter capacity formula is derived for a degraded compound source with an arbitrary (possibly infinite) set of source states and a finite set of marginal states.