The daily returns of four African countries' stock market indices for the period January 2, 2000, to December 31, 2014, were employed to compare the GARCH(1,1) model and a newly proposed Maximal Overlap Discreet Wavelet Transform (MODWT)-GARCH(1,1) model. The results showed that although both models fit the returns data well, the forecast produced by the GARCH(1,1) model underestimates the observed returns whereas the newly proposed MODWT-GARCH(1,1) model generates an accurate forecast value of the observed returns. The results generally showed that the newly proposed MODWT-GARCH(1,1) model best fits returns series for these African countries. Hence the proposed MODWT-GARCH should be applied on other context to further verify its validity.