In this work, we have proposed that the neural synapses and neurons can be realized by utilizing spin waves (SWs) as information carrier. The SWs is excited by spin torque nano-oscillator (STNO), and detected with several different physical mechanisms: 1) tunneling magnetic-resistance 2) spin pumping and 3) inverse spin hall effect. The proposed SWs based synapses and neurons can be further combined together to form a neuromorphic computation system with crossbar structure. Possible ultra low power consumption and ultra high speed are the advantage of our proposed SWs based synapses and neurons.