We present GR-NLP-TOOLKIT, an open-source natural language processing (NLP) toolkit developed specifically for modern Greek. The toolkit provides state-of-the-art performance in five core NLP tasks, namely part-of-speech tagging, morphological tagging, dependency parsing, named entity recognition, and Greeklish-to-Greek transliteration. The toolkit is based on pre-trained Transformers, it is freely available, and can be easily installed in Python (pip install gr-nlp-toolkit). It is also accessible through a demonstration platform on HuggingFace, along with a publicly available API for non-commercial use. We discuss the functionality provided for each task, the underlying methods, experiments against comparable open-source toolkits, and future possible enhancements. The toolkit is available at: https://github.com/nlpaueb/gr-nlp-toolkit