FTP from Unix to mainframe is no problem provided the mainframe supports FTP and the associated TCP/IP stack. Some mainframes use EBCDIC instead of ASCII for text file so you may have to convert your data.
I assume that you want to run the script at the Unix end. For this I usually recommend using Expect to drive the FTP session. I use this to maintain my own web-site. Recently, I have come across LFTP which may be a better alternative as it includes a scripting language.
I would avoid running FTP directly from a shell script. This approach will usually work fine until the FTP session fails. Then it becomes difficult to work out was has worked and what has failed.
I have put some links below. Before downloading any of these packages you should check your Unix/Linux distribution. You may find that you already have the software.