This　correspondence　proposes　a　novel　multiple-antenna　linearly　weighted　(MALW)　spectrum　sensing　method　with　random　arrivals　of　primary　users　(PUs)　for　cognitive　users.　The　method　first　constructs　a　local　test　statistic　for　each　antenna　based　on　the　assumption　that　the　PU　is　randomly　arriving,　and　then　calculates　the　estimated　optimum　coefficient　for　every　local　test　statistic　and　finally　gets　the　total　test　statistic　by　linearly　combing　the　local　test　statistics　and　the　estimated　optimum　coefficients.　Given　false　alarm　probability,　the　proposed　method　calculates　the　corresponding　threshold　according　to　Neyman-Pearson　criteria　and　makes　the　final　decision　by　comparing　the　total　test　statistic　with　the　threshold.　Simulation　results　prove　the　validity　and　the　superiority　of　the　proposed　MALW　method　when　the　PU　is　arriving　randomly　during　the　spectrum　sensing　period.