Neural text-to-SQL models have achieved remarkable performance in translating natural language questions into SQL queries. However, recent studies reveal that text-to-SQL models are vulnerable to task-specific perturbations. Previous curated robustness test sets usually focus on individual phenomena. In this paper, we propose a comprehensive robustness benchmark based on Spider, a cross-domain text-to-SQL benchmark, to diagnose the model robustness. We design 17 perturbations on databases, natural language questions, and SQL queries to measure the robustness from different angles. In order to collect more diversified natural question perturbations, we utilize large pretrained language models (PLMs) to simulate human behaviors in creating natural questions. We conduct a diagnostic study of the state-of-the-art models on the robustness set. Experimental results reveal that even the most robust model suffers from a 14.0% performance drop overall and a 50.7% performance drop on the most challenging perturbation. We also present a breakdown analysis regarding text-to-SQL model designs and provide insights for improving model robustness.