Thanks a lot User137! Your tips were very valuable! =)

To achieve the best result I did use the 17 pixels around the current pixel.

Here is the final code :

Code:
  procedure BoxBlur(var Texture: zglPTexture);
  var
    X, Y: Integer;
    yLine, xLine, yLine2, yLine3: PByteArray;
    data: PByteArray;
    realWidth: Integer;
    realHeight: Integer;
  begin
    realWidth := Round(Texture.Width / Texture.U);
    realHeight := Round(Texture.Height / Texture.V);
    tex_GetData(Texture, data);

    for Y := 1 to realHeight - 2 do
    begin
      yLine := @data[realWidth * (Y) * 4]; // Current Line
      yLine2 := @data[realWidth * (Y - 1) * 4]; // Prior Line
      yLine3 := @data[realWidth * (Y + 1) * 4]; // Next Line

      xLine := @data[realWidth * Y * 4];

      for X := 1 to realWidth - 2 do
      begin
        xLine^[X * 4] := ((xLine^[X * 4] + xLine^[(X - 1) * 4] + xLine^[(X + 1) * 4] + yLine^[(X - 1) * 4] + yLine^[(X + 1) * 4] + yLine2^[(X - 1) * 4] + yLine2^[(X + 1) * 4] + yLine3^[(X - 1) * 4]
              + yLine3^[(X + 1) * 4]) + (xLine^[(X - 2) * 4] + xLine^[(X + 2) * 4] + yLine^[(X - 2) * 4] + yLine^[(X + 2) * 4] + yLine2^[(X - 2) * 4] + yLine2^[(X + 2) * 4] + yLine3^[(X - 2) * 4]
              + yLine3^[(X + 2) * 4])) div 17;

        xLine^[X * 4 + 1] := ((xLine^[X * 4 + 1] + xLine^[(X - 1) * 4 + 1] + xLine^[(X + 1) * 4 + 1] + yLine^[(X - 1) * 4 + 1] + yLine^[(X + 1) * 4 + 1] + yLine2^[(X + 1) * 4 + 1] + yLine2^[(X - 1)
              * 4 + 1] + yLine3^[(X + 1) * 4 + 1] + yLine3^[(X - 1) * 4 + 1]) + (xLine^[(X - 2) * 4 + 1] + xLine^[(X + 2) * 4 + 1] + yLine^[(X - 2) * 4 + 1] + yLine^[(X + 2) * 4 + 1] + yLine2^[
              (X + 2) * 4 + 1] + yLine2^[(X - 2) * 4 + 1] + yLine3^[(X + 2) * 4 + 1] + yLine3^[(X - 2) * 4 + 1])) div 17;

        xLine^[X * 4 + 2] := ((xLine^[X * 4 + 2] + xLine^[(X - 1) * 4 + 2] + xLine^[(X + 1) * 4 + 2] + yLine^[(X - 1) * 4 + 2] + yLine^[(X + 1) * 4 + 2] + yLine2^[(X + 1) * 4 + 2] + yLine2^[(X - 1)
              * 4 + 2] + yLine3^[(X + 1) * 4 + 2] + yLine3^[(X - 1) * 4 + 2]) + (xLine^[(X - 2) * 4 + 2] + xLine^[(X + 2) * 4 + 2] + yLine^[(X - 2) * 4 + 2] + yLine^[(X + 2) * 4 + 2] + yLine2^[
              (X + 2) * 4 + 2] + yLine2^[(X - 2) * 4 + 2] + yLine3^[(X + 2) * 4 + 2] + yLine3^[(X - 2) * 4 + 2])) div 17;

      end;
    end;

    tex_SetData(Texture, data, 0, 0, realWidth, Texture.Height);
    FreeMem(data);
  end;