The linear-chain states of $^{14}$C are theoretically investigated by using the antisymmetrized molecular dynamics. The calculated excitation energies and the $alpha$ decay widths of the linear-chain states were compared with the observed data reported by the recent experiments. The properties of the positive-parity linear-chain states reasonably agree with the observation, that convinces us of the linear-chain formation in the positive-parity states. On the other hand, in the negative-parity states, it is found that the linear-chain configuration is fragmented into many states and do not form a single rotational band. As a further evidence of the linear-chain formation, we focus on the $alpha$ decay pattern. It is shown that the linear-chain states decay to the excited states of daughter nucleus $^{10}{rm Be}$ as well as to the ground state, while other cluster states dominantly decay into the ground state. Hence, we regard that this characteristic decay pattern is a strong signature of the linear-chain formation.
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