System call should be done in the python process to avoid blocking Vim

autoload/tmuxcomplete.vim

@@ -13,7 +13,7 @@ endfunction
 
 let s:script = expand('<sfile>:h:h') . "/sh/tmuxcomplete"
 
-function! tmuxcomplete#completions(base, capture_args, splitmode)
+function! s:build_command(base, capture_args, splitmode)
     let pattern   = '^' . escape(a:base, '*^$][.\') . '.'
     let list_args = get(g:, 'tmuxcomplete#list_args', '-a')
     let grep_args = tmuxcomplete#grepargs(a:base)
@@ -29,6 +29,16 @@ function! tmuxcomplete#completions(base, capture_args, splitmode)
         let command .= ' -e' " exclude current pane
     endif
 
+    return command
+endfunction
+
+function! tmuxcomplete#getcommand(base, splitmode)
+    return s:build_command(a:base, s:capture_args, a:splitmode)
+endfunction
+
+function! tmuxcomplete#completions(base, capture_args, splitmode)
+    let command = s:build_command(a:base, a:capture_args, a:splitmode)
+
     let completions = system(command)
     if v:shell_error != 0
         return []

rplugin/python3/deoplete/sources/tmuxcomplete.py

@@ -1,6 +1,7 @@
 from .base import Base
 
 import deoplete.util
+from subprocess import check_output
 
 class Source(Base):
     def __init__(self, vim):
@@ -12,5 +13,6 @@ def __init__(self, vim):
         self.rank = 4
 
     def gather_candidates(self, context):
-        return [{ 'word': x } for x in
-                self.vim.call('tmuxcomplete#gather_candidates')]
+        command = self.vim.call('tmuxcomplete#getcommand', '', 'words')
+        words = check_output(['sh', '-c', command]).decode('utf-8').splitlines()
+        return [{ 'word': x } for x in words]