The current study aimed at investigating the comorbidity between reading disability (RD) and mathematical disability (MD) in a non-alphabetic language context. Over 1,900 Chinese first graders were screened on their reading and mathematics achievement twice. Children who scored consistently below the 10^th percentile in reading and/or mathematics were identified as RD and/or MD respectively. A subsample of these children, together with a group of typically-achieving children, were further assessed on their cognitive capacities. Results suggested that while there were cognitive deficits that were specifically found in RD (shifting) versus MD (spatial working memory, inhibition, processing speed, visual attention) groups, deficits in naming speed was found in both RD and MD groups. The cognitive profile of the comorbid group was an additive combination of those of the two single LD groups. The findings suggest that RD and MD are two dissociable learning disabilities with distinct cognitive profiles. Effective screening and intervention can be developed based on the cognitive profiles of different disability groups.