In　this　paper,　we　introduced　a　family　of　distributions　with　a　very　flexible　shape　named　generalized　scale　mixtures　of　generalized　asymmetric　normal　distributions　(GSMAGN).　We　investigated　the　main　properties　of　the　new　family　including　moments,　skewness,　kurtosis　coefficients　and　order　statistics.　A　variant　of　the　expectation　maximization　(EM)-type　algorithm　was　established　by　combining　the　proflie　likihood　approach　(PLA)　with　the　classical　expectation　conditional　maximization　(ECM)　algorithm　for　parameter　estimation　of　this　model.　This　approach　with　analytical　expressions　in　the　E-step　and　tractable　M-step　can　greatly　improve　the　computational　speed　and　efficiency　of　the　algorithm.　The　performance　of　the　proposed　algorithm　was　assessed　by　some　simulation　studies.　The　feasibility　of　the　proposed　methodology　was　illustrated　through　two　real　datasets.　©　2024　the　Author(s),　licensee　AIMS　Press.