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A topology optimization method for designing phononic Dirac-like cones and topological insulators by achieving the specific modes at specific frequencies is developed. At first, the Dirac-like cone is created by degenerating one monopolar mode and two dipolar modes at the desired frequency. It is demonstrated that the optimized phononic crystals with Dirac-like exhibit exotic zero-index wave manipulation phenomena. Next, by triggering the dipolar and quadrupolar modes simultaneously to form the double Dirac cone and then breaking it to realize band inversion, topological phase transition around the desired frequency is achieved. The robust one-way edge transport associated with topological phase transition is presented. Recently, two types of dispersions have been aroused great attention: Dirac cone and topological phase transition.Dirac cone is a linear dispersion resulting from the solution of the Dirac equation when the effective mass of a particle equals to zero. [2] It can be also found at the boundary of the Brillouin zone in classical wave systems, e.g., photonic crystals [3,4] and PCs. [5]