A single valued neutrosophic set (SVNS), which is the subclass of a neutrosophic set, can be considered as a powerful tool to express the indeterminate and inconsistent information in the process of decision making. Then, correlation is one of the most broadly applied indices in many fields and also an important measure in data analysis and classification, pattern recognition, decision making and so on. Therefore, we propose another form of correlation coefficient between SVNSs and establish a multiple attribute decision making method using the correlation coefficient of SVNSs under single valued neutrosophic environment. Through the weighted correlation coefficient between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, two illustrative examples are employed to illustrate the actual applications of the proposed decision-making approach.