In　extreme　learning　machine　(ELM),　a　large　number　of　hidden　nodes　are　required　due　to　the　randomly　generated　hidden　layer.　To　improve　network　compactness,　the　ELM　with　smoothedl(0)regularizer　(ELM-SL0　for　short)　is　studied　in　this　paper.　Firstly,　thel(0)regularization　penalty　term　is　introduced　into　the　conventional　error　function,　such　that　the　unimportant　output　weights　are　gradually　forced　to　zeros.　Secondly,　the　batch　gradient　method　and　the　smoothedl(0)regularizer　are　combined　for　training　and　pruning　ELM.　Furthermore,　both　the　weak　convergence　and　strong　convergence　of　ELM-SL0　are　investigated.　Compared　with　other　existing　ELMs,　the　proposed　algorithm　obtains　better　performance　in　terms　of　estimation　accuracy　and　network　sparsity.