  We study a linearly coupled Schr\"{o}dinger system in $\R^N(N\leq3).$ Assume
that the potentials in the system are continuous functions satisfying suitable
decay assumptions, but without any symmetry properties and the parameters in
the system satisfy some suitable restrictions. Using the Liapunov-Schmidt
reduction methods two times and combing localized energy method, we prove that
the problem has infinitely many positive synchronized solutions, which extends
the result Theorem 1.2 about nonlinearly coupled Schr\"{o}dinger equations in
\cite{aw} to our linearly coupled problem.
