We investigate the linear-chain structures in highly excited states of 14 C using a generalized molecular orbital model, by which we incorporate an asymmetric configuration of three α clusters in the linear-chain states. By applying this model to the 14 C system, we study the 10 Be+α correlation in the linear-chain state of 14 C. To clarify the origin of the 10 Be+α correlation in the 14 C linearchain state, we analyze linear 3α and 3α+n systems in a similar way. We find that a linear 3α system prefers the asymmetric 2α+α configuration, whose origin is the many body correlation incorporated by the parity projection. This configuration causes an asymmetric mean field for two valence neutrons, which induces the concentration of valence neutron wave functions around the correlating 2α. A linear-chain structure of 16 C is also discussed.