Summary: Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation with distributed delays, \[ x'(t)= x(t)\Big[a(t)-\sum_{i=1}^n a_i(t)\int_{-T_i}^0 x(t+\theta)\, \mathrm{d}\mu_i(\theta)- \sum_{j=1}^m b_j(t) \int_{-\widehat{T}_j}^0 x'(t+\theta)\,\mathrm{d}\nu_j(\theta)\Big], \] where the coefficients \(a, a_i ,b_j\) are continuous and periodic functions, with the same period. The values \(T_i, \widehat{T}_j\) are positive, and the functions \(\mu_i, \nu_j\) are nondecreasing with \(\int_{-T_i}^0\,\text{ d} \mu_i=1\) and \(\int_{-\widehat{T}_j}^0\,\text{ d} \nu_j=1\).