Single　crystals　of　the　noncentrosymmetric　borate　CaBiGaB2O7　were　synthesized　by　conventional　solid　state　reaction.　The　purity　of　the　crystal　was　checked　by　x-ray　powder　diffraction.　The　optical　properties　were　measured　by　analyzing　the　diffuse　reflectance　data　obtained　with　a　Shimadzu　UV-3101PC　double-beam,　double-monochromator　spectrophotometer.　We　find　a　steep　absorption　edge　confirming　its　semiconducting　nature.　The　optical　band　gap　obtained　by　extrapolation　of　a　linearlike　absorption　edge　was　roughly　2.9　eV　consistent　with　the　observed　pale　yellow　color　of　the　sample.　Theoretical　calculations　based　on　the　structural　model　built　from　our　measured　atomic　parameters　have　been　performed　using　the　all-electron　full　potential　linearized　augmented　plane　wave　method.　The　generalized　gradient　approximation　(GGA)　of　the　exchange　correlation　potential　as　given　by　Engel-Vosko　GGA　is　used.　The　frequency-dependent　complex　dielectric　function　was　calculated　and　the　origin　of　some　of　the　spectral　peaks　is　discussed.　The　linear　optical　properties　show　strong　uniaxial　anisotropy　and　birefringence　that　favors　large　second　order　susceptibility.　Our　calculations　show　that　the　complex　second　order　nonlinear　optical　susceptibility　tensor　chi((2))(322)(omega)　is　the　dominant　component　having　the　largest　total　Re　chi((2))(322)(0)　value　of　about　1.8　pm/V.