The aim of this paper is to investigate numerical solutions of modified improved Boussinesq (MIBq) equationutt=uxx+alpha mml:mfenced close=")" open="(" separators=""u3xx+uxxtt, which is a modified type of Boussinesq equations born as an art of modelling water-wave problems in weakly dispersive medium such as surface waves in shallow waters or ion acoustic waves. For this purpose, Lumped Galerkin finite element (LGFE) method, an effective, accurate, and cost-effective method, is applied to model equation by the aid of quadratic B-spline basis. The efficiency and accuracy of the method are tested with two problems, namely, propagation solitary wave and interaction of two solitary waves. The error normsL(2)andL(infinity)have been computed in order to measure how "accurate" the numerical solutions. Also, the stability analysis has been investigated.