We present the feasibility of structured-light-based diffuse optical tomography (DOT) to quantify the breast density with an extensive simulation study. This study is performed on multiple numerical breast phantoms built from magnetic resonance imaging (MRI) images. These phantoms represent realistic tissue morphologies and are given typical breast optical properties. First, synthetic data are simulated at five wavelengths using our structured-light-based DOT forward problem. Afterwards, the inverse problem is solved to obtain the absorption images and subsequently the chromophore concentration maps. Parameters, such as segmented volumes and mean concentrations, are extracted from these maps and used in a regression model to estimate the percent breast densities. These estimations are correlated with the true values from MRI, r=0.97, showing that our new technique is promising in measuring breast density.