While there is evidence that human-like characteristics in robots could benefit child-robot interaction in many ways, open questions remain about the appropriate degree of human likeness that should be implemented in robots to avoid adverse effects on acceptance and trust. This study investigates how human likeness, appearance and behavior, influence children’s social and competency trust in a robot. We first designed two versions of the Furhat robot with visual and auditory human-like and machine-like cues validated in two online studies. Secondly, we created verbal behaviors where human likeness was manipulated as responsiveness regarding the robot’s lexical matching. Then, 52 children (7-10 years old) played a storytelling game in a between-subjects experimental design. Results show that the conditions did not affect subjective trust measures. However, objective measures showed that human likeness affects trust differently. While low human-like appearance enhanced social trust, high human-like behavior improved children’s acceptance of the robot’s task-related suggestions. This work provides empirical evidence on manipulating facial features and behavior to control human likeness in a robot with a highly human-like morphology. We discuss the implications and importance of balancing human likeness in robot design and its impacts on task performance, as it directly impacts trust-building with children.