Recurrent laryngeal nerve paralysis is the most common and serious complication after thyroid cancer surgery. The objective of this study was to report the advantages of the vein wrapping technique for nerve reconstruction in patients with thyroid cancer invading the recurrent laryngeal nerve and its effects on postoperative phonatory function. The subjects were three patients who underwent resection of the recurrent laryngeal nerve during surgical extirpation of papillary thyroid cancer. Free ansa cervicalis nerve graft or direct neurorrhaphy with a vein wrapping technique was used to facilitate nerve regeneration, protect the anastomosed nerve site mechanically, and prevent neuroma formation. One-year postoperative laryngoscopic examination revealed good vocal cord mobility. Maximum phonation time ($19.5{pm}0.3$ sec) was longer than a previously-reported value in conventional reconstruction patients ($18.8{pm}6.6$ sec). The present phonation efficiency index ($7.88{pm}0.78$) was higher than that previously calculated in conventional reconstruction ($7.59{pm}2.82$). The mean value of the Voice Handicap Index-10 was 6, which was within the normal range. This study demonstrates improvement in phonation indices measured 1 year after recurrent laryngeal nerve reconstruction. Our results confirm that the vein wrapping technique has theoretical advantages and could be favored over conventional reconstruction techniques for invenerate nerve injuries.