Let X be a smooth complex projective variety of dimension n and let L-1,..., Ln-i be ample line bundles on X, where i is an integer with 0 <= i <= n - 1. In the previous paper, we defined the i-th sectional geometric genus g(i)(X, L-1,..., Ln-i) of (X, L-1 ,..., Ln-i). In this part II. we will investigate a lower bound for g(i)(X, L-1,..., Ln-i). Moreover we will study the first sectional geometric genus of (X, L-1,..., Ln-1).