Is there a way to turn on ES6/ES7 syntax support in vscode?

This link helped a lot. Adding the jsconfig.json file to the the project didn't help much or rather it's not the best solution. Go to file > preferences > settings. In the settings.json file add this line:

"jshint.options": { "esversion": 6 }

Also you can also enable this setting for the entire project by creating a .jshintrc file in your project's root and adding this content.

{
  "esversion": 6
}

Currently, the only way to use ES6 and ES7 features is to use Typescript.

On the other hand, here you can see that there is a feature request for ES6 and ES7

Adding to the above answers...

As per Docs of VS Code..

Make sure that you place the jsconfig.json at the root of your JavaScript project and not just at the root of your workspace. Below is a jsconfig.json file which defines the JavaScript target to be ES6 and the exclude attribute excludes the node_modules folder.

{
    "compilerOptions": {
        "target": "ES6"
    },
    "exclude": [
        "node_modules"
    ]
}

Here is an example with an explicit files attribute.

{
    "compilerOptions": {
        "target": "ES6"
    },
    "files": [
        "src/app.js"
    ]
}

The files attribute cannot be used in conjunction with the exclude attribute. If both are specified, the files attribute takes precedence.

also try editing the "target" property in tsconfig.json

{
  "compilerOptions": {
    "target": "es5",//es6
    "module": "system",
    "moduleResolution": "node",
    "sourceMap": true,
    "emitDecoratorMetadata": true,
    "experimentalDecorators": true,
    "removeComments": false,
    "noImplicitAny": false
  },
  "exclude": [
    "node_modules",
    "typings/main",
    "typings/main.d.ts"
  ]
}

It's quite easy, at the root of your project create a jsconfig.json file and write this object in it:

{
    "compilerOptions": {
        "target": "ES6",
        "module": "commonjs"
    }
}