Syntactic parsing is a highly linguistic processing task whose parser requires training on treebanks from the expensive human annotation. As it is unlikely to obtain a treebank for every human language, in this work, we propose an effective cross-lingual UD parsing framework for transferring parser from only one source monolingual treebank to any other target languages without treebank available. To reach satisfactory parsing accuracy among quite different languages, we introduce two language modeling tasks into dependency parsing as multi-tasking. Assuming only unlabeled data from target languages plus the source treebank can be exploited together, we adopt a self-training strategy for further performance improvement in terms of our multi-task framework. Our proposed cross-lingual parsers are implemented for English, Chinese, and 22 UD treebanks. The empirical study shows that our cross-lingual parsers yield promising results for all target languages, for the first time, approaching the parser performance which is trained in its own target treebank.