An approach of transmission network expansion planning with embedded constraints of short circuit currents and N-1 security is proposed in this paper. The problem brought on by the strong nonlinearity property of short circuit currents is solved with a linearization method based on the DC power flow. The model can be converted to a mixed-integer linear programming problem, realizing the optimization of planning model that considers the constraints of linearized short circuit currents and N-1 security. To compensate the error caused by the assumptions of DC power flow, the compensation factor is proposed. With this factor, an iterative algorithm that can compensate the linearization error is then presented. The case study based on the IEEE 118-bus system shows that the proposed model and approach can be utilized to: optimize the construction strategy of transmission lines; ensure the N-1 security of the network; and effectively limit the short circuit currents of the system.