We report on the first study and a proof-of-principle demonstration of aperiodically alternating-Δβcouplers in LiNbO3 waveguides whose switching behavior can be engineered with a high degree of freedom. A high fabrication-tolerance and broad working-bandwidth electro-optic (EO) coupler is developed based on a unique Δβ scheme derived using a simulated annealing algorithm and realized in Ti-diffused aperiodically poled lithium niobate (APPLN) waveguides. The waveguide fabrication tolerance and the working bandwidth (149.2 nm) of the APPLN EO coupler are found to be increased by 2.7 and 2.4 times, respectively, over that of a conventional periodically alternating-Δβ (PPLN) coupler for ≥99% power transfer efficiency under a fixed switching voltage at the 1550 nm band. The results even hold for a domain poling-width error of ≤9%. An interesting APPLN EO coupler capable of working on a certain coupling state over a broad voltage operating range is also studied. The technology developed in this work should enable the production of coupler devices whose switching characteristics can be tailored and realized with much more relaxed fabrication and bandwidth control, which would be beneficial for the application in efficient and compact integrated-optic circuits/systems.