We present a method of effectively concealing data in two quantization levels representing blocks based on Absolute Moment Block Truncation Coding (AMBTC) using Hamming code. The reason for choosing AMBTC as the cover media is that AMBTC is not only easily compressible by simple arithmetic operations, but is also efficient for exchanging data in small portable terminals, such as smart devices, because compression efficiency and image quality are satisfactory. AMBTC is expressed in the form of a $trio (a, b, BM)$, where $a$ and $b$ are quantization levels and BM is a bitmap. The quantization level is a pixel value used as a representative value when dividing an image into $4 \times 4$ blocks. Bai \& Chang introduced a method of hiding data using Hamming code. However, this method presented a problem with efficiency compared to the existing methods. In this paper, in order to improve the problem of this method, we minimize the error that occurs when concealing the data using the optimized Hamming code lookup table. We verified that the performance of the proposed method is satisfactory in terms of embedding capacity and quality of the image through sufficient experimental results.