Fluorescence resonance energy transfer has emerged as a powerful technique in developing semiconductor quantum dot based sensors. Here we report FRET from CdSe (core) and CdSe/ZnS (core/shell) QD donors to cresyl violet dye acceptor employing steady state and time resolved spectroscopy techniques. The FRET efficiency of these systems was investigated as function of size of the QDs as well as surface chemistry conditions. Interestingly, the FRET efficiency did not follow the linear dependence on the spectral overlap integral as expected from the Förster's theory. This nonlinear dependence is presumed to be due to the role of QD surface states in the energy transfer from the QDs to the acceptor molecule.