Steady, laminar three-dimensional (3D) magnetohydrodynamic (MHD) flow of an electrically conducting fluid in a circular pipe under the both magnetic and electrical field are studied. External magnetic and electrical fields are applied perpendicular to the flow direction and each other while the fluid motion is subjected to constant pressure gradient along axial-direction in the present paper. Fluent 14.0, the finite element software based on the finite volume approach was used to calculate the 3D fluid dynamics and electromagnetic field partial differential equations iteratively. The originality of this work is that, in addition to magnetic field; the effect of electrical field on MHD flows is being examined with help of user defined function (UDF) code. The magnetic field leads to decrease in the velocity of flow, whereas the electrical field applied with magnetic field acted to increase and decrease the velocity of flow depending on the direction of applied external electrical field. The obtained results were depicted graphically and discussed.