Looking at the Apple, Mozilla and Mozilla again documentation, the functionality seems to be limited to handle only string key/value pairs.

A workaround can be to stringify your object before storing it, and later parse it when you retrieve it:

var testObject = { 'one': 1, 'two': 2, 'three': 3 };

// Put the object into storage
localStorage.setItem('testObject', JSON.stringify(testObject));

// Retrieve the object from storage
var retrievedObject = localStorage.getItem('testObject');

console.log('retrievedObject: ', JSON.parse(retrievedObject));