Higher income may be a precondition for healthy environment and better health services. There is considerable evidence and academic debate regarding relationships between per capital income and various health indicators including child mortality. In this paper, we proposed a twovariable reciprocal regression model to establish the relationship between child mortality and per capital income. The method of ordinary least squares and some statistical inference were employed to analyse critically and ascertain the relationships between the two variables. From the analysis, it was discovered by the test of significance of regression, that there exist a relationship between the child mortality and per capital income at 5percent level of significance.