在OP的编辑之后：

var now = new Date();

var start = new Date(now.getFullYear(), 0, 0);

var diff = now - start;

var oneDay = 1000 * 60 * 60 * 24;

var day = Math.floor(diff / oneDay);

console.log('Day of year: ' + day);

编辑：上面的代码会失败时，now是3月26日和10月29日之间的日期now的时间是凌晨1点之前（如零时59分59秒）。这是因为该代码未考虑夏令时。

var now = new Date();

var start = new Date(now.getFullYear(), 0, 0);

var diff = (now - start) + ((start.getTimezoneOffset() - now.getTimezoneOffset()) * 60 * 1000);

var oneDay = 1000 * 60 * 60 * 24;

var day = Math.floor(diff / oneDay);

console.log('Day of year: ' + day);