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An attempt has been made in this paper to identify the research productivity on the bibliometircs subject published from 2013 to 2017 in the Web of Science database. 1422 research articles on bibliometrics published in various library science journals and indexed in the web of science database is considered as a basis of data for the study. In this article we made an attempt to analyze the pattern of publication of 1422 research articles. The study involved on various bibliometric components such as annual growth rate, authorship pattern, distribution of contribution by country wise, language wise, institution wise, most prolific author in the field, high productivity of Journals, etc are studied. On an average 284 articles were published in each year during the study period and highest number of articles are recorded in the year 2016. Further, USA is a contributed the highest number of research articles (22.2%). The journal “scientometric” ranks as the first core journals in the subject of library science by contributing 37% of the total publications. Finally, the study concluded that there has been consistent growth of literature in the field of bibliometric studies and also given data set well fitted with the Bradford law of scattering of literature.