Dielectric metamaterial is promising for significantly enhanced optical nonlinearity for its strongly localized Mie-resonant mode. Here, we theoretically and experimentally studied a hybrid metamaterial exhibiting extraordinary optical transmission (EOT) behavior, in which the transmission amplitude and frequency can be modulated. The EOT of the perforated metal sheet with subwavelength aperture is induced with a dielectric cuboid by setting them in a close proximity and exploiting the first-order Mie-resonant mode. The electromagnetic wave is effectively coupled to the subwavelength aperture by properly placing the dielectric cuboid, and the transmission intensity can be enhanced more than 150 times. Meanwhile, we employed the nonlinear effect of the dielectric cuboid to modulate the operation band of the EOT. Hopefully, our work can inspire innovations for the research of the light-matter interactions, electromagnetic light switching devices and filter devices.