This study aims to develop a numerical scheme in collocated Cartesian grids to solve the level set equation together with the incompressible two-phase flow equations. A seventh-order accurate upwinding combined compact difference (UCCD7) scheme has been developed for the approximation of the first-order spatial derivative terms shown in the level set equation. Developed scheme has a higher accuracy with a three-point grid stencil to minimize phase error. To preserve the mass of each phase all the time, the temporal derivative term in the level set equation is approximated by the sixth-order accurate symplectic Runge-Kutta (SRK6) scheme. All the simulated results for the dam-break, Rayleigh-Taylor instability, bubble rising, two-bubble merging, and milkcrown problems in two and three dimensions agree well with the available numerical or experimental results.