We study the average supremum of some random Dirichlet polynomials D _N (t) = ∑ _n=1 ^N ε _n d(n)n ^-σ-it , where (ε_n ) is a sequence of independent Rademacher random variables, the weights d(n) satisfy some reasonable conditions and 0 ∼ σ ∼1/2. We use an approach based on methods of stochastic processes, in particular the metric entropy method developed in [8].