A new approach to sustainable project scheduling for public institutions is proposed. The approach is based on experts’ opinions on three aspects of sustainability of project activities (human resources consumption, material consumption and negative influence on local communities), expressed by means of Z-fuzzy numbers. A fuzzy bicriterial optimization model is proposed, whose objective is to obtain a project schedule of an acceptable sustainability degree and of acceptable duration and cost. The model was inspired and is illustrated by a real-world infrastructure project, implemented in 2019 by a public institution in Poland.