Transaction Log file .ldf is too small Current database is almost 200GB however the transaction log file is only 4.1GB. 
I am worried if this influences the performance of databse and how could it be solved. 

When I do this query

DECLARE @DatabaseName VARCHAR(50) ;
  SET @DatabaseName = 'dbname'
  SELECT name ,
    recovery_model_desc ,
    log_reuse_wait_desc
  FROM  sys.databases
  WHERE name = @DatabaseName

Show Recovery Model = Simple, Log Reuse Wait = Nothing. 


Anyone has a knowledge why the log file is so small, and does this influences on the performance?
The file size of the transaction log is in no way related to the size of the data files, so the question you've asked is really a non-starter to troubleshoot performance.

The transaction log stores the physical operations that happen to the database. Since the database is in SIMPLE recovery, the log only holds on to the operations until a CHECKPOINT occurs -- at this time, the transaction log that's no longer required is internally cleared and can be reused. The physical file size would not need to change unless the active transactions take up more space than is physically available. (Yes, I've simplified things a bit in this paragraph.)

That said, your transaction log could suffer from performance issues if there are too many VLFs, likely from the result of small autogrowth increments -- see my answer here for a bit of information about how the transaction log works internally with regards to this. It also depends what the workload is for this database (many small transactions, or few large transactions).