This brief paper investigates the stability and L∞-gain of positive fractional-order singular systems (FOSSs) with time-varying delays. Based on the Drazin inverse of singular matrices, an equivalent auxiliary system is developed to avoid the singularity problem, and a sufficient and necessary criterion ensuring the positivity of delayed FOSSs is established. Furthermore, the asymptotic stability of FOSSs is analyzed using the positivity and monotonicity of system solutions instead of the fractional Lyapunov stability theorem. Finally, a simulation experiment utilizing electrical circuit system is carried out to justify the rationality of the results.