This paper analyzes the admittance-dissipativity of dual-sequence current control for grid-connected voltage-source converters (VSCs). The output admittance model of dual-sequence current control is first developed in the stationary reference frame by using complex vectors. Impacts of digital filters used within current control and voltage-feedforward (VFF) control loops, and of the delay compensation at the fundamental frequency, are then evaluated. It is found that the cascaded use of sequence-decomposition filter (SDF) and the low-pass filter (LPF) in the VFF control loop adds a non-dissipative region in the output admittance, and the fundamental-frequency delay-compensation further worsens the dissipativity. An analytical design method for the LPF is then developed to mitigate the non-dissipative region, which lowers the instability risks and improves the stability robustness of dual-sequence current control under different grid conditions. Lastly, simulations and experimental results corroborate theoretical analyses.