To improve the accuracy of the simulation calculation of an HVDC transmission system based on state-space method, a method for an HVDC system considering a snubber circuit is proposed. Valve current and snubber current are used as state variables to model a thyristor. The voltage transformation relation of a converter transformer under different working conditions is expressed as a unified form by a correlation matrix, so as to establish the state-space model of converter and converter transformer, from which the state-space expression of primary equipment in an HVDC system is derived simultaneously with the DC line model. Also, a calculation method of trigger angle in the control system is proposed. A data interaction process between the primary equipment system and the control side system is introduced. As a result, a high-precision solution of the mathematical model of an HVDC system is realized. Finally, algorithm results realized by Matlab are compared with the simulation results of PSCAD, and the solving accuracy of the primary system can reach 99.99%. This work is supported by the Science and Technology Project of Southern China Power Grid (No. ZBKJXM20180104).