我建立了一个模板webapi项目试了下是没问题得。
排查思路：

• 检测Global.asax

protected void Application_Start()
{
            AreaRegistration.RegisterAllAreas();
            GlobalConfiguration.Configure(WebApiConfig.Register);
            FilterConfig.RegisterGlobalFilters(GlobalFilters.Filters);
            RouteConfig.RegisterRoutes(RouteTable.Routes);
            BundleConfig.RegisterBundles(BundleTable.Bundles);
}

• RouteConfig中的路有模板设置

public static void RegisterRoutes(RouteCollection routes)
{
            routes.IgnoreRoute("{resource}.axd/{*pathInfo}");            
            routes.MapRoute(
                name: "Default",
                url: "{controller}/{action}/{id}",
                defaults: new { controller = "Home", action = "Index", id = UrlParameter.Optional }
            );
}