Development of memristor-based device in 2008 has encouraged scientists and engineers to perform brain-inspired cognitive tasks on the hardware level. Memristor is a resistor with memory which has some similarity like a synapse in our brain and can be fabricated in a 3-dimensional array with high density. This allows memristors to be used in parallel processing application like pattern recognition. Memristor-based neuromorphic systems have neuron and memristor integrated together as a fundamental unit which works like biological neuron and synapses. This unit is repeated in large number and interacts with each other to perform the complex functionalities. A double barrier memristor device has been developed by the Institute of Electrical Engineering and Information Technology, the University of Kiel which shows a continuous change in resistance when a consecutive write voltage is applied. This device has to be integrated with CMOS neuron to develop potentiation and depression. An integrate & fire neuron chip with spiking circuit has been designed and fabricated in AMS350 nm process. DBMD has been integrated with Neuron ASIC and the measurement shows Long-Term Potentiation (LTP) on hardware level which can be used for a larger network to mimic functionalities of the brain.