Introduction: Research into amyotrophic lateral sclerosis often focuses on the purely medical aspects of the disease, without paying attention to patient’s experience, suffering and difficulties they face on a daily basis. The aims of this study were to describe resilience and investigate its relationship with psychological well-being, measured as depression and anxiety in a sample of adult patients with different levels of amyotrophic lateral sclerosis severity. Methods: This was a cross-sectional study conducted in Sardinia (Italy). The study took place between January 2017 and June 2017. Thirty-one amyotrophic lateral sclerosis patients (55% males; mean age = 63.8 years; standard deviation, SD = 9.6) were included in the study. They were recruited from one of the main regional centres for amyotrophic lateral sclerosis treatment on the island, and represented the total population of amyotrophic lateral sclerosis patients in the territory in question. Their age ranged from 37 to 81 years (M = 63.81; SD = 9.63). Assisted by the staff, they completed the Connor–Davidson Resilience Scale and the Hospital Anxiety and Depression Scale. Results: A significant, strongly negative correlation was found between resilience and psychological well-being. Moreover, the level of depression decreased with the increasing time after the diagnosis, but it increased with patient’s age. Conclusions: In view of the results obtained, it can be hypothesised that proper psychological support designed to promote the activation of resilience resources could help an amyotrophic lateral sclerosis patient cope with negative emotions, pain, and difficulties that accompany the disease. Furthermore, these findings suggest assessing resilience in amyotrophic lateral sclerosis patients to better characterise the risk of mood disorders and direct mental health screening efforts.