convert string to datetime with form yyyy-MM-dd HH:mm:ss in C#

I think your parsing worked. The problem is when converting back to string. You can provide the desired format in parameter :

DateTime date = DateTime.ParseExact("2010-01-01 23:00:00", "yyyy-MM-dd HH:mm:ss", CultureInfo.InvariantCulture);
string formattedDate = date.ToString("yyyy-MM-dd HH:mm:ss")
Console.WriteLine(formattedDate);

By default (without a specified format), it uses formatting information derived from the current culture.

Because 2014-01-01 23:00:00 IS 2014-01-01 11:00:00 PM.

Better explanation

You are implicitly calling DateTime.ToString(), which by default uses the General ("G") format, which in the en-US culture is MM/dd/yyyy hh:mm:ss tt.

If you want to display the time in a different format, you need to specify it:

string s = DateTime.ParseExact("2010-01-01 23:00:00", "yyyy-MM-dd HH:mm:ss", CultureInfo.InvariantCulture);
Console.WriteLine(s.ToString("yyyy-MM-dd HH:mm:ss");

Or since you're using the same format string, just store it:

string format = "yyyy-MM-dd HH:mm:ss";
DateTime dt = DateTime.ParseExact("2010-01-01 23:00:00", format , CultureInfo.InvariantCulture);
Console.WriteLine(s.ToString(format);