A problem called boson sampling---sampling from the probability distribution of several identical bosons scattered by some linear unitary process---has raised strong interest recently. Despite the simplicity of its structure, boson sampling is a computational hard problem which can not be efficiently simulated on classical computers. By now, several boson sampling experiments have been reported. However, in all of these experiments, boson sampling is realized by implementing the procedure literally instead of being simulated with other systems. It is well known that quantum processes, which are hard to be simulated on classical computers, can be efficiently simulated with controllable quantum devices. In this sense, boson sampling itself should be able to be well simulated with controlled quantum systems. Here we present a method to efficiently simulate boson sampling with qubit systems which are directly applicable to the standard quantum computing model. The two motivations to simulate boson sampling with qubit system are described below. Firstly, the standard quantum computing model is based on qubit system. By simulating boson sampling with qubits, one can run boson sampling on a quantum computer. Secondly, compared with the complex output quantum state that boson sampling process renders, the well-defined multi-qubit output quantum state our method provides is much easier for manipulation and processing. As our method makes the output state of boson sampling more usable, it might help theorists find some new applications for boson sampling. Besides presenting the theory, we have also experimentally demonstrate our scheme using photonic qubits. The experimental results reproduce the probability distribution of boson sampling quite well, which is in accordance with the theoretical expectation.