In this paper, we propose a newly constructed binary code to correct one deletion and one insertion error that simultaneously occur at any position in a codeword. We first investigated all cases of one deletion and one insertion error. Three constraints in the proposed construction were used for determining the bit values and positions of all error cases. Furthermore, we propose the decoding procedure with two parallel decoding algorithms and explain the specific decoding procedure. To the best of the authors’ knowledge, our work is the first trial to provide an efficient code construction design to correct one deletion and one insertion error occurring in a codeword.