In a standard compressive sampling (CS) setup, we develop a universal algorithm where multiple CS reconstruction algorithms participate and their outputs are fused to achieve a better reconstruction performance. The new method is called universal algorithm for CS (UACS) that is iterative in nature and has a restricted isometry property (RIP) based theoretical convergence guarantee. It is shown that if one participating algorithm in the design has a converging recurrence inequality relation then the UACS also holds a converging recurrence inequality relation over iterations. An example of the UACS is presented and studied through simulations for demonstrating its flexibility and performance improvement.