I have a Canon Pixma MX882 printer. The printer show a message to notify me that I need to replace the black ink (low black ink level), but I used the remain ink completely until the printer stop to p

SOURCE: Pixma MP780 Printer, not printing

sometimes those measures of ink levels are not very accurate. actually they're usually rather far off... try a new cartridge Usually the easiest solution.

SOURCE: Missing Colors

This is a simple problem just reset your printer's color management settings!!!!!!!!!!!!!!!!!!!! :-)

SOURCE: Faulty Ink Cartridge?

You can try this, but maybe a new print head is needed.
OK, Canon will hate me for posting this.

1. Remove ink cartridges
2. Remove print head
3. go to sink or tub (stainless steel, not plastic type), pick up a roll of paper towel on the way.
4. Fold several layers of paper towel and place on flat surface.
5. Run hot water until HOT!
6. Turn hot water back to a dribble.
7. Run the dribbling hot water through print head, be careful not to wet the gold contacts.
8.When water running through print head is clear, place print head on paper towel.
9. Repeat number 7 and 8 until no colour shows on paper towel.
10. Gently DAB print head (DO NOT WIPE) inside and out with dry paper towel until dry.
11. I normally replace print head after drying, but you may wish to let it air dry overnight.
12. Replace print head in printer and install cartridges
13. Start printing.

I do this to all 4 of my Canon printers every 6 months or so.

If any colour fails to print after this process it means your print head probably needs replacing.

SOURCE: Print head remains clogged canon pixma iP 4000

I have successfully managed to clean the print head with isopropyl alcohol by placing a flexible plastic tube over the cartridge seat, filling the tube partially with the alcohol, then blowing very hard through the tube. The alcohol does not appear to harm anything.

SOURCE: Canon MP800 PGBK black ink will

I have the same problem.  I turned off the printer, then selected "auto head alignment from the printer's maintenance menu and it worked! 
Menu -> Maintenance/Settings -> Maintenance -> Auto Head Align