This is perfectly normal. Check the PMT data sheet: http://www.hamamatsu.com/resources/pdf/etd/R3809U-50_TPMH1067E09.pdf

If you want to lower the dark count, you must decrease the PMT temperature  e.g. by using a thermoelectric cooling unit accessory.

I am relatively new to TCSPC but background is normal with any PMT.

I suggest collecting background signal anyway for the same integration time that you use for collection so you know the source is just the PMT. You can also use the value measured to input into the analysis software you are using.

You are unclear whether the MCPT is operated at low temperature or not. High voltage should never be applied to an MCPT at RT. Your dark counts with the MCPT temperature around -30C, should be no more than 100, when the count rate is in 10^4, and you have accumulated more than 10^3 counts.

Thank you all, I really appreciate.

The MCP-PMT is running at Room Temperature. We do not have thermoelectric cooler.

Here are some more solutions.

1. Collect the emission decay for longer time atleast 5,000 or 10,000 counts at the peak. The S/N ratio would be better and you can fit the data better after subtracting the background.

2. If possible, Increase the concen of the dye, S/N will improve. Ensure that there are no complications due to increased concentration.

3. Just check the Hamamatsu datasheet and see if the background is in the expected range. Higher background can also be because of some stray light reaching the detector. Just check if there is any stray light reaching the detector. Blocking the stray light will reduce the background.

4. Also one can reduce the background counts by cooling the MCP-PMT as mentioned above.

Hope this helps.