The all-optical switching characteristics of three-core nonlinear directional waveguide couplers (NLDCs) with Gaussian type and exponential type variable coupling coefficient (VCC) are presented. Their transmission features are investigated numerically. It is shown that， for the three-core VCC NLDCs, the power can switch completely between guide 1 and guide 3; however 100% power output cannot be achieved for guide 2. The switching curves of three-core NLDCs with VCC are sharper than those of their two-core counterparts with same maximum coupling coefficient. It is also shown that the sidelobes in the post-switching region, which exist in the parallel nonlinear directional couplers, can be suppressed with three-core NLDC with VCC.