In this paper the problem of random disturbance attenuation capabilities in linear continuous systems is studied. It is supposed  that the system operates under random disturbances with bounded σ-entropy level. σ-entropy norm indicates a performance index of the continuous system on the set of the random signals with bounded σ-entropy. This paper presents a time-domain solution to the calculation of σ-entropy norm of the continuous linear time-invariant system. σ-entropy norm |||F|||σ is defined after solving coupled matrix equations: one algebraic Riccati equation, one nonlinear equation over log determinant function, and two Lyapunov equations.