uses
  {...,} FMX.GifUtils;

type
  TFormMain = class(TForm)
    Image: TImage;
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
    FGifPlayer : TGifPlayer;
  end;

{...}

implementation

{$R *.fmx}

procedure TFormMain.FormCreate(Sender: TObject);
begin
   FGifPlayer:=TGifPlayer.Create(Self);
   FGifPlayer.Image:=Image;
   FGifPlayer.LoadFromFile('D:\image.gif');
   FGifPlayer.Play;
end;