Tinnitus is a perception of sound in the brain without any external stimulus. Tinnitus patients often complain of more efforts required in listening. They may be ineffective in inhibiting their attention, driven to irrelevant ringing sounds in their ear rather than attending to the relevant target speech stimulus. The study's objective was to evaluate an allocation of cognitive resources among tinnitus patients for concurrent tasks required for understanding speech using an objective dual-task paradigm to assess listening effort. We recruited 40 participants with mild to moderately severe sloping sensorineural hearing loss within 60-70 years. They were subgrouped into control and clinical groups. The clinical group had a severe degree of tonal tinnitus bilaterally. The objective listening task used listening effort, and a subjective questionnaire to assess the effort in listening was assessed by each study participant. The results indicated poorer recognition and reduced recall scores in a clinical group than the control group in each signal-to-noise ratio. The recall score in objective listening effort measurement was strongly correlated with subjective questions assessed effort in listening among the clinical group at each signal-to-noise ratio. However, in the control group, the correlation was to a mild degree at 0 dB signal-to-noise ratio only. Annoyance caused by tinnitus disrupts attention, thereby limiting the effective use of cognitive resources for concurrent speech processing and recalling reflected in the listening effort task.