This paper presents a new approach for model-order reduction of linear time varying system based on expanding the time-varying system in the right half plane of the s-domain. The proposed algorithm is developed through introducing Krylov-Subspace-based reduction to time-varying transfer functions. The proposed algorithm does not require solution of large system of equations to construct a basis for the time varying moments. Instead, it computer such a basis through time-domain integration of the corresponding linear time-varying differential algebraic equations. Numerical experiments show that expanding in the right-half plane compress the transient phase of the response of these equations by several order of magnitude.