[{"Fio":"Ivanov","Date":"January 16","Parametr":"200"},{"Fio":"Petrov","Date":"January 16","Parametr":"300"},{"Fio":"Ivanov","Date":"February 16","Parametr":"100"},{"Fio":"Petrov","Date":"February 16","Parametr":"150"},{"Fio":"Ivanov","Date":"March 16","Parametr":"400"},{"Fio":"Petrov","Date":"March 16","Parametr":"500"},{"Fio":"Sidorov","Date":"March 16","Parametr":"300"}]

[{"Month":"January","Ivanov":"200","Petrov":"300"},{"Month":"February","Ivanov":"100","Petrov":"150"},{"Month":"March","Ivanov":"400","Petrov":"500","Sidorov":}]

[js]
... ваш код...
[/js]

var a = [{
	"Fio": "Ivanov",
	"Date": "January 16",
	"Parametr": "200"
}, {
	"Fio": "Petrov",
	"Date": "January 16",
	"Parametr": "300"
}, {
	"Fio": "Ivanov",
	"Date": "February 16",
	"Parametr": "100"
}, {
	"Fio": "Petrov",
	"Date": "February 16",
	"Parametr": "150"
}, {
	"Fio": "Ivanov",
	"Date": "March 16",
	"Parametr": "400"
}, {
	"Fio": "Petrov",
	"Date": "March 16",
	"Parametr": "500"
}, {
	"Fio": "Sidorov",
	"Date": "March 16",
	"Parametr": "300"
}];

var months = {};

a.forEach(function(item) {
	months[ item['Date'] ] = true;
});

var b = [];

Object.keys(months).forEach(function(month) {
	var newObj = {};
	newObj['Month'] = month.replace(/[\d+\s]/g, '');

	a.forEach(function(obj) {
		if (obj['Date'] == month) {
			newObj[ obj['Fio'] ] = obj['Parametr'];
		}
	});

	b.push(newObj);
});

console.log( JSON.stringify(b) );

<script>
 var data = [{
        Fio: "Ivanov",
        Date: "January 16",
        Parametr: "200"
    }, {
        Fio: "Petrov",
        Date: "January 16",
        Parametr: "300"
    }, {
        Fio: "Ivanov",
        Date: "February 16",
        Parametr: "100"
    }, {
        Fio: "Petrov",
        Date: "February 16",
        Parametr: "150"
    }, {
        Fio: "Ivanov",
        Date: "March 16",
        Parametr: "400"
    }, {
        Fio: "Petrov",
        Date: "March 16",
        Parametr: "500"
    }, {
        Fio: "Sidorov",
        Date: "March 16",
        Parametr: "300"
    }],
    obj = {},
    data = data.reduce(function(b, c) {
        var a = c.Date.split(" ")[0];
        void 0 === obj[a] && (obj[a] = b.length, b[b.length] = {Month: a});
        a = obj[a];
        b[a][c.Fio] = c.Parametr;
        return b
    }, []);

document.write(JSON.stringify(data))
  </script>