The laser light propagation inside the conical target has been studied by three-dimensional particle-in-cell simulations. It is found that the existence of under-dense plasma significantly affects the light propagation and the generation of relativistic electrons. The laser light can be focused at the tip of the cone and the intensity increases up to tens of times in the focal spot. With the under-dense plasma the laser light focused intensity is decreased. The existence of under-dense plasmas favors the relativistic electron generation in the laser conical target interaction in enhancing the number and energy of relativistic electrons.