How to change the color of highlighted misspelled word?

Try this:

 :hi SpellBad guibg=#ff2929 ctermbg=224

• guibg is for GUI
• ctermbg is for TERM

You can use the hi (short for :help highlight) command in your ~/.vimrc. The general structure is:

hi SpellBad    ctermfg=015      ctermbg=000     cterm=none      guifg=#FFFFFF   guibg=#000000   gui=none

The cterm is for terminal vim and the gui is for gVim. The fg stands for foreground and is the color of the letters and the bg stands for background and is the color behind the letters.

Terminal colors can be 0-15 for standard terminal colors (8 normal and 8 bright) or 0-255 for terms supporting 256 colors, like xterm-256colors. The gui colors are in hexadecimal format. xterm-color-table is a useful reference for both 256 and hexadecimal colors. The final option can be used to specify bold, italic, or none (neither).

In your case, it might be simplest to set the foreground to black to make the letters stand out. First, find a word that's mispelled with :set spell and then typing asdflkjasldf or something. Then type :hi SpellBad ctermfg=000 guifg=#000 and see if that's a solution you like. If not, use the xterm-color-table or another color reference to find a color you do like.