Recently, the study of resilience has become more significant because people are more aware of the consequences of natural and human-made disasters. The well-fare of our communities highly relies on continuous access to the vital services supplied by the critical infrastructure systems (CIS). However, the continuous operation of these CIS can be adversely affected by different disruptive events. To survive these disruptions, being resilient is very important for CIS. Generally, the resilience of a CIS can be classified into two parts, including soft resilience and hard resilience. Hard resilience represents the behavior of the technical part of the CIS, and soft resilience represents people and the organization running the CIS before, during, and after the disruption. In this paper, the focus is on the soft part of resilience, which means organizational resilience. Resilient organizations advance despite experiencing situations that are unexpected, uncertain, often adverse, and usually unstable. From an organizational perspective, an organization's resilience is driven by four generic indicators: the Sense of ownership, flexibility, creativity, and initiative. Many factors influence these indicators with different importance levels (weights). A practical index-based methodology is introduced to estimate the organizational resilience index (ORI) by adopting these generic indicators and influencing factors. In the developed methodology, expert judgment is used to quantify the effect of influencing factors. Furthermore, fuzzy sets theory is used to capture the uncertainty and bias of expert judgment. Finally, the application of the proposed methodology is illustrated using a real case study.