Data efficiency is a critical challenge for cross-lingual task-oriented dialogue state tracking (DST) due to high cost of collecting large amount of task-related labeled training set for specific language. Therefore, we focus on adapting high-performance source language DST to target language by using only bilingual dictionary, without accessing labeled target data. We propose a novel data efficient cross-lingual DST framework (ECO-DST), which consists of cross-lingual encoder and language independent decoder. To support cross-lingual zero-shot adaptation, we leverage two advanced methods in encoder: 1) pre-trained cross-lingual model XLM-RoBERTa (XLM-R), 2) dynamic local phrase code-switching data augmentation for cross-lingual representation alignment. We evaluate the proposed method on The Ninth Dialogue System Technology Challenge (DSTC9) cross-lingual tasks. For target language DST, we compare our proposed framework with submitted systems in DSTC9, our model achieves state-of-the-art result on CrossWOZ dataset and promising result on MultiWOZ 2.1 dataset. Meanwhile on source language DST, the same model keeps competitive performance compared with original source DST model.