The current experiment was carried out to compare REML-based to ANOVA-based methods (Griffing, Cockerham, Henderson) in estimation of crossbreeding genetic parameters in chicken experiments. The current experiment involved a full 4*4 diallel crossing among four Egyptian breeds (Alexandria (AA), Fayoumi (FF), Matrouh (MM) and Golden Montazah (GG). The studied traits were body weight at hatch (BWH), body weight at 4 weeks of age (BW4), body weight at 8 weeks of age (BW8) and body weight at 12 weeks of age (BW12). The general comparison among models showed the superiority of REML-based method, especially in prediction ability with significant difference. A close comparison between REML and Griffing methods showed consistency between both methods with the advantage of accurate estimation and prediction ability of the REML-based method. The analysis of the empirical data showed the superiority of the AA line in general combining ability (GCA). The genotypes of MG, FM and AG showed the highest specific combining ability (SCA) in the end of the experiment at 12 weeks of age.