Abstract: A  new approach is presented to construct infinite families of singular k-tight optimal double loop networks.As its applications,the authors give some infinite families of singular k-tight optimal double loop networks when N(t)=3t2+(2i-1)t+B,B=k2+k-m,1≤i≤3 and N(t)∈Ii(t) for  integers k>1/2m+（3+(2i-1)2）/24,m≥（i-i2-1）/3.

Key words: double loop networks, diameter, tight optimal, infinite family, singular k-tight optimal