Hyperspectral imaging (HSI) can combine morphological and molecular information, yielding potential for real-time and high throughput multiplexed fluorescent contrast agent imaging. Multiplexed readout from targets, such as cell surface receptors overexpressed in cancer cells, could improve both sensitivity and specificity of tumor identification. There remains, however, a need for compact and cost effective implementations of the technology. We have implemented a low-cost wide-field multiplexed fluorescence imaging system, which combines LED excitation at 590, 655 and 740 nm with a compact commercial solid state HSI system operating in the range 600 - 1000 nm. A key challenge for using reflectance-based HSI is the separation of contrast agent fluorescence from the reflectance of the excitation light. Here, we illustrate how it is possible to address this challenge in software, using two offline reflectance removal methods, prior to least-squares spectral unmixing. We made a quantitative comparison of the methods using data acquired from dilutions of contrast agents prepared in well-plates. We then established the capability of our HSI system for non-invasive in vivo fluorescence imaging in small animals using the optimal reflectance removal method. The HSI presented here enables quantitative unmixing of at least four fluorescent contrast agents (Alexa Fluor 610, 647, 700 and 750) simultaneously in living mice. A successful unmixing of the four fluorescent contrast agents was possible both using the pure contrast agents and with mixtures. The system could in principle also be applied to imaging of ex vivo tissue or intraoperative imaging in a clinical setting. These data suggest a promising approach for developing clinical applications of HSI based on multiplexed fluorescence contrast agent imaging.