How to change the highlight style in Vim spellcheck?

Spelling errors are highlighted using the SpellBad highlighting group. To get it highlighted as you want, you should put something like

hi clear SpellBad
hi SpellBad cterm=underline
" Set style for gVim
hi SpellBad gui=undercurl

after the last line that is altering the color scheme in your vimrc (it is either set background=(dark|light) or colorscheme {schemename}).

See also :h hl-SpellBad for names and descriptions of other Spell* highlight groups.

The above needs to be typed everytime you set colorscheme. If you wish to avoid it, you should use autocmd.

See https://vi.stackexchange.com/questions/18295/how-to-set-a-colorscheme-that-still-shows-spelling-errors