An ink supplier that supplies ink to a plurality of heads in an ink-jet printing apparatus , comprising: a supply reservoir storing said ink to be supplied to said plurality of heads ; and a discharge pipe having a pump and used for discharging said ink from said supply reservoir , said supply reservoir including: a first horizontal reservoir having a cylindrical shape extending in a direction of alignment of said plurality of heads , and having a plurality of supply ports each communicating with one of said plurality of heads ; and a first vertical reservoir having a side surface provided with a first opening directly or indirectly communicating with one end of said first horizontal reservoir , and having a cylindrical shape with a closed bottom larger in a top-bottom direction than said first horizontal reservoir , said first horizontal reservoir having a bottom surface that is tilted from a horizontal direction at an angle of tilt equal to or greater than 0.3° in such a manner as to extend downward from said one end toward the other end , wherein said first horizontal reservoir includes a first discharge port provided at a bottom portion of said first horizontal reservoir at said other end and communicably connected to said discharge pipe . a supply reservoir storing said ink to be supplied to said plurality of heads ; and a discharge pipe having a pump and used for discharging said ink from said supply reservoir , said supply reservoir including: a first horizontal reservoir having a cylindrical shape extending in a direction of alignment of said plurality of heads , and having a plurality of supply ports each communicating with one of said plurality of heads ; and a first vertical reservoir having a side surface provided with a first opening directly or indirectly communicating with one end of said first horizontal reservoir , and having a cylindrical shape with a closed bottom larger in a top-bottom direction than said first horizontal reservoir , said first horizontal reservoir having a bottom surface that is tilted from a horizontal direction at an angle of tilt equal to or greater than 0.3° in such a manner as to extend downward from said one end toward the other end , wherein said first horizontal reservoir includes a first discharge port provided at a bottom portion of said first horizontal reservoir at said other end and communicably connected to said discharge pipe . a first horizontal reservoir having a cylindrical shape extending in a direction of alignment of said plurality of heads , and having a plurality of supply ports each communicating with one of said plurality of heads ; and a first vertical reservoir having a side surface provided with a first opening directly or indirectly communicating with one end of said first horizontal reservoir , and having a cylindrical shape with a closed bottom larger in a top-bottom direction than said first horizontal reservoir , said first horizontal reservoir having a bottom surface that is tilted from a horizontal direction at an angle of tilt equal to or greater than 0.3° in such a manner as to extend downward from said one end toward the other end , wherein said first horizontal reservoir includes a first discharge port provided at a bottom portion of said first horizontal reservoir at said other end and communicably connected to said discharge pipe . <EOS>