We present a new technique for direct measurements of degenerate two-photon absorption (TPA) spectra of two-photon absorbing materials including non-fluorescent samples. This technique is based on the use of an intense single continuum-generation beam as the coherent white-light source with specially flattened spectral distribution. The different spectral components of the continuum beam are spatially dispersed and then passed through the sample material along different pathways so that nondegenerate TPA processes among different input spectral components can be avoided. By comparing the input and transmitted continuum spectral distributions, the TPA spectrum for a given sample can be obtained. As an example, the continuous TPA spectrum (from 550 to 1000 nm) is measured for a novel two-photon-absorbing compound (AF-389) which exhibits an extremely high TPA cross-section value of ∼1 × 10- 20 cm4/GM, or ∼249 GM, around ∼800-nm spectral range in femtosecond regime.