1，建立一个CorsHandler类

public class CorsHandler : DelegatingHandler
{
const string Origin = "Origin";
const string AccessControlRequestMethod = "Access-Control-Request-Method";
const string AccessControlRequestHeaders = "Access-Control-Request-Headers";
const string AccessControlAllowOrigin = "Access-Control-Allow-Origin";
const string AccessControlAllowMethods = "Access-Control-Allow-Methods";
const string AccessControlAllowHeaders = "Access-Control-Allow-Headers";

protected override Task<HttpResponseMessage> SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
{
bool isCorsRequest = request.Headers.Contains(Origin);
bool isPreflightRequest = request.Method == HttpMethod.Options;
if (isCorsRequest)
{
if (isPreflightRequest)
{
return Task.Factory.StartNew<HttpResponseMessage>(() =>
{
HttpResponseMessage response = new HttpResponseMessage(HttpStatusCode.OK);
response.Headers.Add(AccessControlAllowOrigin, request.Headers.GetValues(Origin).First());

string accessControlRequestMethod = request.Headers.GetValues(AccessControlRequestMethod).FirstOrDefault();
if (accessControlRequestMethod != null)
{
response.Headers.Add(AccessControlAllowMethods, accessControlRequestMethod);
}

string requestedHeaders = string.Join(", ", request.Headers.GetValues(AccessControlRequestHeaders));
if (!string.IsNullOrEmpty(requestedHeaders))
{
response.Headers.Add(AccessControlAllowHeaders, requestedHeaders);
}

return response;
}, cancellationToken);
}
else
{
return base.SendAsync(request, cancellationToken).ContinueWith<HttpResponseMessage>(t =>
{
HttpResponseMessage resp = t.Result;
resp.Headers.Add(AccessControlAllowOrigin, request.Headers.GetValues(Origin).First());
return resp;
});
}
}
else
{
return base.SendAsync(request, cancellationToken);
}
}
}

2、在Application_Start()里面配置

//jsonp跨域
GlobalConfiguration.Configuration.MessageHandlers.Add(new CorsHandler());

OK，完美解决。