In order to coordinate the economy and voltage quality of a meshed AC/VSC-MTDC system, a new corrective security-constrained multi-objective optimal power flow (SC-MOPF) method is presented in this paper. A parallel SC-MOPF model with N-1 security constraints is proposed for corrective control actions of the meshed AC/DC system, in which the minimization of the generation cost and voltage deviation are used as objective functions. To solve this model, a novel parallel bi-criterion evolution indicator based evolutionary algorithm (BCE-IBEA) algorithm is developed to seek multiple well-spread Pareto-optimal solutions through the introduction of parallel computation. In this process, a least absolute shrinkage and selection operator (Lasso)-based N-1 contingency filtering scheme with a composite security index is developed to efficiently screen out the most severe cases from all contingencies. And thereby, the best compromise solutions reflecting the preferences of different decision makers are automatically determined via an integrated decision making technique. Case studies in the modified IEEE 14- and 300- bus systems demonstrate that the presented approach manages to address this SC-MOPF problem with significantly improved computational efficiency.