We propose a potentially practical scheme for realization of an n-qubit conditional phase flip (CPF) gate and implementation of Grovers search algorithm in an ion-trap system.We demonstrate, both analytically and numerically, that our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability.We also show the merits of the Proposal that the increase of the ion number can improve the fidelity and success probability of the CPF gate.The required operations for a Grover search are very close to the capabilities of current ion-trap techniques.