Let Mn=diag[3pn,3qn] with pn,qn⩾1 for all n⩾1 and let D={(0,0)t,(1,0)t,(0,1)t} . One can generate a Borel probability measure μ{Mn},D=δM1−1D∗δ(M2M1)−1D∗δ(M3M2M1)−1D∗⋯. Such measure μ{Mn},D is called a Moran Sierpinski-type measure. It is known Deng et al (Acta Math. Sin. submitted) that the associated Hilbert space L2(μ{Mn},D) has an exponential orthonormal basis. In this paper, we first characterize all the maximal exponential orthogonal sets for L2(μ{Mn},D) . For such a maximal orthogonal set, we then give some sufficient conditions to determine whether it is an orthonormal basis of L2(μ{Mn},D) or not.