A Brain Computer Interface (BCI) character speller allows human-beings to directly spell characters using eye-gazes, thereby building communication between the human brain and a computer. Current popular BCI character speller systems employ a large number of sensors, which prevents the utilization of such systems in human's daily life. Using sensor selection methods to select appropriate sensor subsets from an initial large sensor set can reduce the number of sensors needed to acquire brain signals without losing the character spelling accuracy, thereby promoting the BCI character spellers into people's daily life. However, current sensor selection methods cannot select an appropriate sensor subset such that they can further reduce the number of sensors needed to acquire brain signals without losing the spelling accuracy. To address this issue, we propose a novel sensor selection method based on a specific Convolutional Neural Network (CNN) we have devised. Our method uses a parametric backward elimination algorithm which uses our devised CNN as a ranking function to evaluate sensors and eliminate less important sensors. We perform experiments on three benchmark datasets and compare the minimal number of sensors selected by our proposed method and other selection methods to acquire brain signals while keeping the spelling accuracy the same as the accuracy achieved when the initial large sensor set is used. The results show that the minimal number of sensors selected by our method is lower than the minimal number of sensors selected by other methods in most cases. Compared with the minimal number of sensors selected by other methods, our method can reduce this number with up to 44 sensors.