Instrumented objects (e.g., smart mattress) are attractive technologies in the field of long-term vital signs monitoring because of their unobtrusiveness. Among the existing sensors that can be employed to develop smart mattress, Fiber Bragg grating sensors (FBGs) are one of the most promising ones. Their particular characteristics (i.e., high-sensitivity, flexibility, multiplexing capability and immunity to electromagnetic fields) allowed the widespread use in the field of cardiorespiratory monitoring. In the present study, we developed a mattress embedding an array of five FBGs to record breathing-related body movements for respiratory rate (RR). We evaluated the feasibility of the proposed mattress for RR monitoring during quiet breathing and tachypnea in two different positions (i.e., supine and prone). In both the positions and under the two breathing conditions, all the FBGs allow the RR monitoring with mean absolute error (MAE) lower than 0.26 bpm compared against RR estimated from the reference instrument.