Process　monitoring　is　a　common　strategy　for　monitoring　the　industrial　production　operation　state.　It　can　detect　abnormal　conditions　in　industrial　processes　and　provide　certain　guidance　for　production.　Many　classical　data-driven　process　monitoring　approaches　neglect　the　non-Gaussian　and　nonlinearity　of　the　data.　For　solving　the　above　problems,　this　paper　designs　an　overcomplete　broad　learning　system　(OBLS)　with　incremental　learning　ability.　The　method　combines　multiple　fault　data　into　one　data　matrix.　Then　the　overcomplete　approach　is　employed　to　capture　the　non-Gaussian　information　from　the　original　data　to　obtain　a　mixed　matrix.　Next,　the　weights　of　the　OBLS　network　are　trained　according　to　the　extracted　feature　matrix　containing　non-Gaussian　information　and　its　corresponding　fault　label.　Meanwhile,　the　nonlinearity　of　the　data　is　addressed　by　the　OBLS　network.　Finally,　the　incremental　learning　capabilities　of　the　OBLS　network　enable　it　to　be　updated　quickly　when　new　fault　samples　are　added　to　the　training　set　without　entire　retraining　process.　The　experimental　results　in　numerical　examples,　penicillin　fermentation　simulation　platform　and　real-world　industrial　process　demonstrate　the　superiority　and　feasibility　of　the　OBLS　model.