Three-dimensional (3D) photonic crystals with complete photonic band gap (PBG) are fascinating due to the possibility of controlling light in all directions. Realizing such photonic crystals is nontrivial due to symmetry requirements and associated fabrication challenges. Liquid crystalline cubic blue phases (BPs) are soft 3D photonic crystals with an incomplete PBG due to the low refractive index contrast (<0.1). The present work attempts to drive a cubic BP towards a complete PBG via a simple approach of high refractive index nanoparticle-doping. The photonic band diagrams and reflection spectra of the nanoparticle-doped BP simulated using the finite element method show an increased PBG width, a parameter that quantifies the complete PBG. The reflection spectra obtained from UV-Vis-NIR spectroscopy show an increase (by a factor of >2) in PBG width for the nanoparticle-doped BP, validating the simulations. The findings are explained based on increased refractive index contrast (∼1.4) due to the nanoparticles getting trapped in the cores of disclination lines that make up the BP lattice. The simulations also indicate effective confinement of electric field eigenmodes in the nanoparticle-doped BP leading to high attenuation of the incident light. Further, the iso-frequency contours extracted from the band diagrams exhibit self-collimation and negative refraction of light.