With the advancements in the field of artificial intelligence, speech recognition based applications are becoming more and more popular in the recent years. Researchers working in many areas including linguistics, engineering, psychology, etc. have been trying to address various aspects relating to speech recognition in different natural languages around the globe. Although many interactive speech applications in "well-resourced" major languages are being developed, uses of these applications are still limited due to language barrier. Hence, researchers have also been concentrating to design speech recognition system in various under-resourced languages. Sylheti is one of such under-resourced languages primarily spoken in the Sylhet division of Bangladesh and also spoken in the southern part of Assam, India. This paper has two contributions: i) it presents a new speech database of isolated words for the Sylheti language, and ii) it presents speech recognition systems for the Sylheti language to recognize isolated Sylheti words by applying two variants of neural network classifiers. The performances of these recognition systems are evaluated with the proposed database and the observations are presented.