The　perfect　achievements　have　been　made　for　L-P　(1　＜=　p　＜　+infinity)　risk　estimation,　when　a　density　function　has　compact　support.　However,　there　does　not　exist　L-1　risk　estimation　for　uncompactly　supported　densities　in　general.　Motivated　by　the　work　of　Juditsky　&　Lambert-Lacroix　(A.　Juditsky　and　S.　Lambert-Lacroix,　On　minimax　density　estimation　on　R,　Bernoulli,　10(2004),　187-220)　and　Goldenshluger　&　Lepski　(A.　Goldenshluger　and　O.　Lepski,　On　adaptive　minimax　density　estimation　on　R-d,　Probab.　Theory　Relat.　Fields.,　159(2014),　479-543),　we　provide　an　adaptive　estimate　for　a　family　of　density　functions　not　necessarily　having　compact　supports　in　this　paper.