Biological long short-term memory (B-LSTM) can effectively help human process all kinds of received information. In this work, a memristive B-LSTM circuit which mimics a conversion from short-term memory to long-term memory is proposed. That is, the stronger the signal, the more profound the memory and the higher the output. On this basis, an image binarization circuit using adaptive row threshold algorithm is proposed. It can make the image remain a deep impression on the strong pixel information and effectively filter the relatively weak pixel information. In combination with the function of image binarization, a memristive circuit for eyes state detection is proposed by adding corresponding horizontal projection calculation, subtraction calculation and judgement open or closed eyes modules. The proposed circuit can detect whether there is a blink between two adjacent facial images, which uses the characteristics of memristor to detect the difference of horizontal projection between two images. Due to the use of memristor, the proposed circuit can realize in-memory computing, which fundamentally avoids the problem of storage wall and shorten the execution time. Finally, an expectation application in fatigue driving based on the proposed method is demonstrated, which indicates the practicability of the circuit design in this work.