Artificial intelligence is used for various applications and is promising as an indispensable infrastructure in future societies. Neural networks are representative technologies that imitate human brains and exhibit various advantages. However, the size is bulky, the power is huge, and some advantages are not demonstrated because they are executed on Neumann-type computers. Neuromorphic systems are biomimetic systems from the hardware level to implement neuron and synapse elements, and the size is compact, the power is low, and the operation is robust. However, because the conventional ones are not composed of fully optimized hardware, the power is not yet minimal, and extra control circuits must be used. In this article, we developed a neuromorphic system using memcapacitors and autonomous local learning. By using memcapacitors, the power can be minimal, and by using autonomous local learning, the control circuits to handle the synapse elements can be deleted. First, the memcapacitors are completed in a cross-bar array, where the ferroelectric layers are sandwiched between the horizontal and perpendicular electrodes. The polarization and capacitance exhibit hysteresis due to the dielectric polarization. Next, autonomous local learning is introduced as follows. During the training phase, associative patterns to be memorized are directly sent, relatively high voltages are applied, and dielectric polarizations are induced. During the operation phase, relatively low voltages are applied, and input signals are weighted with the capacitances of the memcapacitors, summed, and transferred as the output signals. Finally, the experimental system is set up, and the experimental results are acquired. The memorized patterns during the training phase, distorted patterns as the input signals during the operation phase, and retrieved patterns as the output signals in the operation phase are shown. Researchers found that the retrieved patterns are completely the same as the memorized patterns. This means that the neuromorphic system works as an associative memory.