Let G be a finite group and r be a prime divisor of the order of G. An irreducible character of G is said to be quasi r-Steinberg if it is non-zero on every r-regular element of G. A quasi r-Steinberg character of degree is said to be weak r-Steinberg if it vanishes on the r-singular elements of In this article, we classify the quasi r-Steinberg cuspidal characters of the general linear group Then we characterize the quasi r-Steinberg characters of and Finally, we obtain a classification of the weak r-Steinberg characters of