You can download the data via this link. It comes in many different products and you will want to know which product is best for your work.

Dear Dr.Lance, thank you for the information, could you please send the link!

 Sorry about that:

Also, there may be an issue with downloading data to outside the US. This might not be the case, but if there is an error, that could be a reason for the error.

http://mirador.gsfc.nasa.gov/cgi-bin/mirador/presentNavigation.pl?project=TRMM&tree=project

Many thanks, Dr.Lance!

Regards,

Alban

TRMM data compatible with GIS can be downloaded from the following sites:

Near-realtime:

ftp://trmmopen.gsfc.nasa.gov/pub/gis

Standard product:

ftp://trmmopen.gsfc.nasa.gov/pub/trmmdata/GIS/

Check out GIOVANNI:

http://giovanni.gsfc.nasa.gov/giovanni/

You can crop, visualize, and download hundreds of RS and reanalysis products including TRMM, and TRMM RT. 

Just to let you know that TRMM  turned  down  on April 2015 and GPM will continue the mission.

Thanks  to Akbari for this important piece of information.

Claudia, choose the format, Level and follow the link below

http://pmm.nasa.gov/data-access/data-downloading

Dear colleagues,

Many thanks for valuable comments and information on this topic!