Summary: In this work, we obtain some new generalized weighted trapezoid and Grüss type inequalities on time scales for parameter functions. Our results give a broader generalization of results due to B. G. Pachpatte [Tamkang J. Math. 34, No. 4, 365–369 (2003; Zbl 1048.26018)]. In addition, the continuous and discrete cases are also considered from which, other results are obtained.