The ExportSheetAsJSON method will convert the active sheet of a Google Spreadsheet to a JSON file and saves the file to your Google Drive. The header (first row) are used as item attributes in the JSON document.

/* From https://gist.github.com/IronistM/8be09ebd4c5a4a58c63b */

function exportSheetAsJSON() {
  var sheet = SpreadsheetApp.getActiveSheet();
  var rows = sheet.getDataRange();
  var numRows = rows.getNumRows();
  var numCols = rows.getNumColumns();
  var values = rows.getValues();

  var output = '';
  output += '{"' + sheet.getName() + '" : {\n';
  var header = values[0];
  for (var i = 1; i < numRows; i++) {
    if (i > 1) output += ' , \n';
    var row = values[i];
    output += '"' + row[0] + '" : {';
    for (var a = 1; a < numCols; a++) {
      if (a > 1) output += ' , ';
      output += '"' + header[a] + '" : "' + row[a] + '"';
    }
    output += '}';
    //Logger.log(row);
  }
  output += '\n}}';
  Logger.log(output);

  DriveApp.createFile(sheet.getName() + '.json', output, MimeType.PLAIN_TEXT);
}