Current research on privacy preservation largely centers on simple first-order systems, while practical applications often involve more complex general linear systems with gain matrices. Developing privacy-preserving algorithms for such systems is therefore of significant engineering value. In this paper, we propose a novel two-phase algorithm for linear continuous-time multiagent systems under strongly connected and balanced directed graphs. The algorithm shields agents’ initial states by employing edge-based perturbations. Rigorous analysis confirms that the algorithm effectively protects initial states against honest-but-curious neighbors. Moreover, numerical simulations further validate the feasibility of the proposed algorithm.