Why parsing a String into Date in Java is slow? Can we accelerate it?

I am reading a text file containing dates, and I want to parse the Strings representing the dates into Date objects in java. What I notice is the operation is slow. Why? is there any way to accelerate it? My file looks like:

2012-05-02 12:08:06:950, secondColumn, thirdColumn
2012-05-02 12:08:07:530, secondColumn, thirdColumn
2012-05-02 12:08:08:610, secondColumn, thirdColumn

I am reading the file line by line, then I am getting the date String from each line, then I am parsing it into a Date object using a SimpleDateFormat as follow:

DataInputStream in = new DataInputStream(myFileInputStream);
BufferedReader  br = new BufferedReader(new InputStreamReader(in));
String strLine;

SimpleDateFormat formatter = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss");
while ((strLine = br.readLine()) != null)
{
    ....Do things....
    Date myDateTime = (Date)formatter.parse(myDateString);
    ...Do things....
}