This article concentrates on designing optimal stealthy attack strategies for cyber-physical systems (CPSs) modeled by the linear quadratic Gaussian (LQG) dynamics, where the attacker aims to increase the quadratic cost maximally and keeping a certain level of stealthiness by simultaneously intercepting and modifying the transmitted measurements. In our work, a novel attack model is developed, based on which the attacker can launch strictly stealthy or ϵ -stealthy attacks. To remain strictly stealthy, the attacker only needs to solve an off-line semidefinite program problem. In such a case, the attack performance is optimal but limited. To achieve a higher desired attack effect than that of the strictly stealthy attack, the attacker sometimes needs to sacrifice the stealthy level. Thus, the ϵ -stealthy attack is analyzed, where an upper bound of the optimal attack performance is obtained by solving a convex optimization problem. Then, an optimal ϵ -stealthy attack is designed to achieve the upper bound, which differs from the existing suboptimal ϵ -stealthy attack for the considered LQG systems. Finally, the simulations are provided to verify the developed results.