We present new Doppler images of both components of the double-lined binary σ2 CrB, based on the high-resolution spectroscopic data collected during 11 nights in 2015 March-April. The observed spectra form two independent data sets with sufficient phase coverage. We apply the least-squares deconvolution to all observed spectra to obtain high signal-to-noise mean profiles, from which we derive the Doppler images of both components of σ2 CrB simultaneously. The surfaces of both F9 and G0 components are dominated by pronounced polar spots. The F9 component exhibits a weak spot at latitude 30° and its mid-to-low latitudes are relatively featureless. The G0 star shows an extended spot structure at latitude 30°, and its surface spot coverage is larger than that of the F9 star, which suggests a higher level of magnetic activity. With the cross-correlation method, we derive a solar-like surface differential rotation on the G0 star of σ2 CrB for the first time, and the surface shear rate is ∆Ω = 0.180 ± 0.004 rad days-1 and α = ∆Ω/Ωeq = 0.032 ± 0.001. We do not obtain a clear surface shear law for the F9 star due to the lack of mid-to-low latitude features, but detect a systematic longitude shift of high-latitude spots, which indicates a slower rotation with respect to the corotating frame.