Semantic parsing is one of the key components of natural language understanding systems. A successful parse transforms an input utterance to an action that is easily understood by the system. Many algorithms have been proposed to solve this problem, from conventional rule-based or statistical slot-filling systems to shift-reduce based neural parsers. For complex parsing tasks, the state-of-the-art method is based on an autoregressive sequence to sequence model that generates the parse directly. This model is slow at inference time, generating parses in O(n) decoding steps (n is the length of the target sequence). In addition, we demonstrate that this method performs poorly in zero-shot cross-lingual transfer learning settings. In this paper, we propose a non-autoregressive parser which is based on the insertion transformer to overcome these two issues. Our approach 1) speeds up decoding by 3x while outperforming the autoregressive model and 2) significantly improves cross-lingual transfer in the low-resource setting by 37% compared to autoregressive baseline. We test our approach on three wellknown monolingual datasets: ATIS, SNIPS and TOP. For cross-lingual semantic parsing, we use the MultiATIS++ and the multilingual TOP datasets.