Broad　Learning　System　(BLS)　is　a　very　fast　and　effective　discriminative　learning　which　is　developed　by　C.　L.　P.　Chen,　Z.　Liu　and　others.　It　avoids　the　shortcomings　of　complex　model　design　and　large　amount　of　calculation　in　deep　learning.　This　paper　studies　the　approximation　capability　of　BLS　for　continuous　functions　defined　on　a　compact　set.　It　is　proved　that　if　the　activation　function　of　the　enhancement　node　of　BLS　is　not　polynomial,　for　any　continuous　function　f(x)　e　C(K)　defined　on　the　compact　set　K,　there　is　limmq→　∞,nk→　∞　f(x)-fw(x)　22=0,　that　is　＞0,　nk　e　N,　mq　e　N＇,　and　parameter　set　w,　so　that　f(x)-fw(x)　22　©　2022　The　authors　and　IOS　Press.