Try to install AndFTP. Then use the provided Intent to download file:
http://www.lysesoft.com/support/forums/viewtopic.php?f=5&t=157
Intent intent = new Intent();
intent.setAction(Intent.ACTION_PICK);
// FTP URL (Starts with ftp://, sftp:// or ftps:// followed by hostname and port).
Uri ftpUri = Uri.parse("ftp://yourftpserver.com");
intent.setDataAndType(ftpUri, "vnd.android.cursor.dir/lysesoft.andftp.uri");
// FTP credentials (optional)
intent.putExtra("ftp_username", "anonymous");
intent.putExtra("ftp_password", "[email protected]");
//intent.putExtra("ftp_keyfile", "/sdcard/dsakey.txt");
//intent.putExtra("ftp_keypass", "optionalkeypassword");
// FTP settings (optional)
intent.putExtra("ftp_pasv", "true");
//intent.putExtra("ftp_resume", "true");
//intent.putExtra("ftp_encoding", "UTF8");
// Download
intent.putExtra("command_type", "download");
// Activity title
intent.putExtra("progress_title", "Downloading files ...");
// Remote files to download.
intent.putExtra("remote_file1", "/remotefolder/subfolder/file1.zip");
intent.putExtra("remote_file2", "/remotefolder/subfolder/file2.zip");
// Target local folder where files will be downloaded.
intent.putExtra("local_folder", "/sdcard/localfolder");
startActivityForResult(intent, 0);