In this study, a new chaotic system and its analog circuit design have been introduced. The circuit of chaotic system has only a memristor, an inductor, a capacitor and a negative resistor. The proposed memristor emulator circuit is based on Operational Transconductance Amplifier (OTA) and it consists of multipliers, resistors, a capacitor and a current conveyor apart from OTAs. We have shown the chaotic behavior of our system with both numerical analyses done in MATLAB environment and an analog circuit analyses using LTspice simulation software. In addition to chaotic (pseudo-periodic) behavior, the periodic spiking behavior of our proposed system by changing a system parameter is also presented. The image cryptology method is carried out to prevent the unauthorized distribution of information and data. In image encryption part, an algorithm is suggested to provide confusion (pixel position permutation) and diffusion (pixel value transformation) operations on the image. A pixel swap method for both row and column is preferred as confusion operation and a logical XOR method for both row and column is done as diffusion operation on the pixels of the image. In order to decrypt the encrypted image, the reversed swap and the reversed XOR operations have been performed. In this way, image encryption and decryption schemes using a chaotic system with OTA based memristor are successfully carried out. Moreover, the security analyses with the help of histogram analysis, correlation coefficient analysis of two adjacent pixels, information entropy analysis and initial condition sensitivity analysis have been done in order to prove that our suggested algorithm is robust against different statistical attacks and exhaustive attack.