您需要从字符串中提取数字，并将其传递给Date constructor：

var x = [{
    "id": 1,
    "start": "\/Date(1238540400000)\/"
}, {
    "id": 2,
    "start": "\/Date(1238626800000)\/"
}];

var myDate = new Date(x[0].start.match(/\d+/)[0] * 1);

这些部分是：

x[0].start                                - get the string from the JSON
x[0].start.match(/\d+/)[0]                - extract the numeric part
x[0].start.match(/\d+/)[0] * 1            - convert it to a numeric type
new Date(x[0].start.match(/\d+/)[0] * 1)) - Create a date object