var arr1 = [{id:'124',name:'qqq',type=3}, 
            {id:'589',name:'www',type=1}, 
            {id:'45',name:'eee',type=1},
            {id:'567',name:'rrr',type=1},
            {id:'124',name:'qqq',type=2}, 
            {id:'589',name:'ddd',type=2}, 
            {id:'45',name:'qqq',type=1},
            {id:'567',name:'vvv',type=3}];

var count = arr.filter(item => item.type === 3 || item.type === 1).length;

您可以使用带有复选标记的Array#reduce并添加比较的值。

var array = [{ id: '124', name: 'qqq', type: 3 }, { id: '589', name: 'www', type: 1 }, { id: '45', name: 'eee', type: 1 }, { id: '567', name: 'rrr', type: 1 }, { id: '124', name: 'qqq', type: 2 }, { id: '589', name: 'ddd', type: 2 }, { id: '45', name: 'qqq', type: 1 }, { id: '567', name: 'vvv', type: 3 }],
    count = array.reduce(function (r, a) {
        return r + +(a.type === 1 || a.type === 3);
    }, 0);

console.log(count);