For a fibration f: X → Z over the filed of complex numbers, Iitaka conjectures κ(X) ≥ κ(Z) + κ(F), where F is the geometric generic fiber of f and κ denotes the Kodaira dimension. The conjecture is usually denoted by Cn,m, n=dim X, m=dim Z. We will introduce the progress of the conjecture on a positive characteristic field, including the recent results of Cn,n-1 and C3,1 on a positive characteristic field. These are joint work with Lei Zhang and Caucher Birkar.