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)∈C(K) defined on the compact set K, there is lim_{mq→ ∞,nk→ ∞}‖f(x)-f_w(x)‖²₂=0, that is ∀ ε>0, ∃nk ∈ N, mq∈N’, and parameter set w, so that ‖f(x)-f_w(x)‖²₂<ε. A reconstructed model of BLS which is combined the CNN network with the BLS is applied to numerical experiments. The semi-supervised broad learning system(SS-BLS) and its algorithm are proposed. Then, SS-BLS and convolution function are combined to establish SS-CBLS, the numerical experiments of SS-CBLS on face classification are carried out by ORL and Yale face database respectively