Quantitative spectroscopy has recently been extended from a contact-probe to wide-area spectroscopic imaging to enable mapping of optical properties across a wide area of tissue. We train quantitative spectroscopic imaging (QSI) to identify cervical high-grade squamous intraepithelial lesions (HSILs) in 34 subjects undergoing the loop electrosurgical excision procedure (LEEP subjects). QSI's performance is then prospectively evaluated on the clinically suspicious biopsy sites from 47 subjects undergoing colposcopic-directed biopsy. The results show the per-subject normalized reduced scattering coefficient at 700 nm (An) and the total hemoglobin concentration are significantly different (p<0.05) between HSIL and non-HSIL sites in LEEP subjects. An alone retrospectively distinguishes HSIL from non-HSIL with 89% sensitivity and 83% specificity. It alone applied prospectively on the biopsy sites distinguishes HSIL from non-HSIL with 81% sensitivity and 78% specificity. The findings of this study agree with those of an earlier contact-probe study, validating the robustness of QSI, and specifically An, for identifying HSIL. The performance of An suggests an easy to use and an inexpensive to manufacture monochromatic instrument is capable of early cervical cancer detection, which could be used as a screening and diagnostic tool for detecting cervical cancer in low resource countries.