Low-density parity-check (LDPC) codes defined over non-binary (NB) finite field GF(2^q) (q>1) achieve better error-correcting performance than binary LDPC codes when the codeword length is moderate. To reduce the complexity for practical applications, codes over lower-order finite fields are of great interest. Previous designs have been focusing on decoders over either the smallest NB field GF(4) or much larger fields, such as GF(32) or higher. Prior optimization techniques are either not applicable or do not lead to efficient designs for codes over lower-order fields, such as GF(8). In this paper, an efficient architecture is developed for the check node processing, which is the most complicated step in NB-LDPC decoding, for the Min-max algorithm over lower-order fields. By utilizing the properties of finite field elements, the max/min comparison results are shared and the number of comparators needed is reduced significantly. Compared to the best prior design, the proposed check node processing has 18.5% smaller area and shorter critical path for an example code over GF(8).