Neoplasms of the appendix are very rare. They usually show glandular or neuroendocrine differentiation, and when they both occur in the same area, it is called a "collision tumor." Low-grade mucinous neoplasms associated with appendiceal diverticula are also uncommon. The appendectomy specimen of a 60-year-old man contained dense and mucoid luminal content on the distal tip, and similarly a solid, yellow, lumen-obscuring tumor with a diameter of 1.5 cm at the base of the appendix was detected. Microscopically, there were three diverticula that comprised herniation of the mucosal layer through the appendiceal wall. Interestingly, all of the diverticula and the normal-appearing appendiceal wall were lined by adenomatous epithelium. The luminal portion had pools of mucin-containing, rare clusters of low-grade epithelium that gave rise to the diagnosis of a "low-grade mucinous neoplasm." The solid-appearing tumor was diagnosed as a "neuroendocrine neoplasm," and there was no transition zone between these two types of tumors. There are some cases that have been reported as low-grade mucinous neoplasms associated with appendicular diverticula and collision tumors consisting both mucinous neoplasms and carcinoid tumors in the literature; our case has a unique appearance with two different types of tumors both in the appendix wall and within multiple diverticula.