Large language models (LLMs) typically provide multilingual support and demonstrate remarkable capabilities in solving tasks described in different languages. However, LLMs can exhibit linguistic discrimination due to the uneven distribution of training data across languages. That is, LLMs struggle to maintain consistency when handling the same task in different languages, compromising both safety equity and knowledge equity. In this paper, we first systematically evaluate the linguistic discrimination of LLMs from two aspects: safety and quality, using a form of metamorphic testing. The metamorphic relationship we examine is that LLMs are expected to deliver outputs with similar semantics when prompted with inputs that have the same meaning. We conduct this evaluation with two datasets based on four representative LLMs. The results show that LLMs exhibit stronger human alignment capabilities with queries in English, French, Russian, and Spanish compared to queries in Bengali, Georgian, Nepali and Maithili. Moreover, for queries in English, Danish, Czech and Slovenian, LLMs tend to produce responses with a higher quality compared to the other languages. Upon these findings, we propose LDFighter, a similarity-based voting method, to mitigate the linguistic discrimination in LLMs. We comprehensively evaluate LDFighter against a spectrum of queries including benign, harmful, and adversarial prompts. The results show that LDFighter significantly reduces jailbreak success rates and improves response quality. All code, data, and the technical appendix are publicly available at: \url{https://github.com/dgl-prc/ldfighter}.