Handwriting recognition is one of the active and challenging areas of research in the field of image processing and pattern recognition. It has many applications that include: a reading aid for visual impairment, automated reading and processing for bank checks, making any handwritten document searchable, and converting them into structural text form, etc. Moreover, high accuracy rates have been recorded by handwriting recognition systems for English, Chinese Arabic, Persian, and many other languages. Yet there is no such system available for offline Kurdish handwriting recognition. In this paper, an attempt is made to design and develop a model that can recognize handwritten characters for Kurdish alphabets using deep learning techniques. Kurdish (Sorani) contains 34 characters and mainly employs an Arabic\Persian based script with modified alphabets. In this work, a Deep Convolutional Neural Network model is employed that has shown exemplary performance in handwriting recognition systems. Then, a comprehensive dataset was created for handwritten Kurdish characters, which contains more than 40 thousand images. The created dataset has been used for training the Deep Convolutional Neural Network model for classification and recognition tasks. In the proposed system, the experimental results show an acceptable recognition level. The testing results reported a 96% accuracy rate, and training accuracy reported a 97% accuracy rate. From the experimental results, it is clear that the proposed deep learning model is performing well and is comparable to the similar model of other languages' handwriting recognition systems.