In this paper, a novel recombination operator, called adaptive hybrid crossover operator (AHX), is designed for tackling continuous multiobjective optimization problems (MOPs), which works effectively to enhance the search capability of multiobjective evolutionary algorithms (MOEAs). Different from the existing hybrid operators that are commonly operated on chromosome level, the proposed operator is executed on gene level to combine the advantages of simulated binary crossover (SBX) with local search ability and differential evolution (DE) with strong global search capability. More opportunities are assigned to DE in the early evolutionary stage for gene-level global search in decision space; whereas, with the generation grows, more chances are gradually allocated to SBX for gene-level local search. The balance between the gene-level global and local search is well maintained by an adaptive control approach in AHX. To validate the effectiveness of AHX, it is studied by substituting the original recombination operators in the four state-of-the-art MOEAs (i.e., NSGA-II, SPEA2, SMS-EMOA, and MOEA/D), and the performance of revised algorithms is significantly improved. Furthermore, AHX is also compared to three recently proposed recombination operators, such as a newly DE inspired (DEI) recombination operator, a learning paradigm based on jumping genes (JGBL) and a bandit-based adaptive operator selection approach (FRRMAB). The experimental studies validate that AHX can be effectively integrated into different frameworks of MOEAs, and performs better than SBX, DE, DEL JGBL and FRRMAB in solving various kinds of MOPs.