Sufficient dynamic Var reserve (DVR) can efficiently enhance the immunity against continuous commutation failures (CCF) to avoid DC blocking and further security accidents in the line-commutated converter (LCC) based HVDC receiving-end power system. This article proposes the problem formulation and efficient solution algorithm for the DVR-constrained coordinated scheduling considering contingencies and wind uncertainties. The DVR sufficiency is proposed for the post-contingency CCF immunity in scheduling problems, which combines the voltage sensitivity-based DVR capacity calculation and the off-line DVR requirement tests. HVDC transmission and W/Var sources are coordinately scheduled to accommodate contingencies and wind uncertainties and to improve the operational economy. The reduced event-based algorithm (REA) is developed to subdivide the complex scheduling problem and reduce the considered constraints for efficient calculation. Case studies demonstrate the guaranteed DVR sufficiency, the improved economy, and the enhanced computational efficiency of the proposed methods.