Two-dimensional electronic spectroscopy (2DES) has emerged as an incisive tool for mapping out energy relaxation pathways in complex molecular systems by determining correlation maps between the excitation and emission frequencies. Its enhanced spectral as well as temporal resolution offer new insights into coupling and energy transfer between closely-spaced energy states, which are often hidden in a one-dimensional transient spectrum. However, a major drawback of the current 2DES technique is that the spectral window of detection is directly limited to the laser bandwidth used, which leads to an incomplete visualization of the full energy landscape of the system. As a solution to this limitation, we present an ultrabroadband 2DES apparatus utilizing a 8-fs, 185-nm bandwidth supercontinuum that covers the entire visible region. We demonstrate the utility of our setup by measuring the 2D spectra of laser dyes absorbing at different regions of the laser spectrum, and the major light-harvesting complex of spinach.