Most proposals for quantum computers are based on linear nearest neighbor (LNN) arrangements where qubits only interact with neighbors. A Toffoli gate is a three-qubit operation, which is used in many quantum applications such as error correction, and algorithms like Shor's factorization. Typically, to implement a Toffoli gate in an LNN architecture, additional operations called swap gates are required to bring the qubits adjacent to each other. We propose a new method to implement a Toffoli gate in LNN arrays without using swap gates. As such, compared to other circuits, the quantum cost of our circuit is much lower.