Convert string in JSON

Although Lorenzo's answer is correct, is there a reason why you are building the string like this? Why not just build the object to start with?

var type = 'text/html';
var content = 'dfg';
var name ='partHtml'

var newPart = {};
newPart[name] = {content_type: type, content: content, type: 'content'};

JSON strings are quoted using ", not '.
Therefore, your example should be:

var newPart = '{"' + name + '": {"content-type" : ' +  type + ', "content": ' + content +  ',"type": "content"}}';
newPart = JSON.parse(newPart);

Or, if you already have everything you need, you could construct the object immediately without using JSON.parse():

var newPart = {"name": {"content-type": type, "content": content, "type": "content"}};

This is a really bad practice and an unsafe method. You just need to create an object.

var newPart = {     
    "content-type" : "text/html",
    "content": "dfg",
    "type": "content"      
}

This is not a valid JSON, so it's not possible to parse it. A valid version would look like this:

{"partHtml": {"content-type": "text/html", "content": "dfg", "type": "content"}}

You can't use the ' character, you need " instead.

JSON strings are quoted using "

`var newStr = '{"' + name + '": {"content-type" : "' + type + '", "content": "' + content + '","type": "content"}}';

var newJson = JSON.parse(newStr);

or

var newJson = eval('(' + newStr + ')');

Just replace this line with your

var newPart = '{\"' + name + '\": {\"content-type\" : \"' +  type + '\", \"content\": \"' + content +  '\",\"type\": \"content\"}}';

you have to be careful while merging strings. Instead of creating a string and face delimitation problems i suggest to create an object instance and assign properties on the fly.

var newPart = {};
newPart.name = {content : content};
newPart.name['content-type'] = type;

and so on..

There's an error in your JSON. text/html is a string, but it's missing quotes.

Try to add them:

var newPart = '{"' + name + '": {"content-type" : "' +  type + '", "content": "' + content +  '", "type": "content"}}'

Please notice that if you want a lint valid JSON, you should use double quotes. Test your JSON in any online tool such as http://jsonlint.com/

{
    "partHtml": {
        "content-type" : "text/html",
        "content": "dfg",
        "type": "content"
    }
}

Moreover, if your variables contain double quotes, you'll get an error while parsing the JSON. This answer would work for your code, but I don't recommend it in real applications because it's a bad practice. For the best practice, please look at the addition that mikeecb did to my answer.