The time-delay signature (TDS) of chaos output in a 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to fiber Bragg grating (FBG) feedback is investigated experimentally. Autocorrelation function (ACF) and mutual information (MI) are used for quantitatively identifying the TDS of chaos. For various bias currents, the TDS evolution with the feedback strength is different, as the FBG provides wavelength-selective feedback. Furthermore, based on the TDS map of the FBG feedback VCSEL (FBGF-VCSEL) in the parameter space of feedback strength and bias current, the optimal TDS suppression regions, where the dominant polarization mode of FBGF-VCSEL locates at the edge of the main lobe of FBG reflection spectrum, have been determined. Finally, for comparative purpose, the TDS of chaos in mirror feedback VCSEL (MF-VCSEL) also has been presented, and the results show that an FBGF-VCSEL possesses better TDS suppression performance than an MF-VCSEL.(XDJK2016D060).