The present study aims to reveal the impact of students' critical thinking and logico-mathematical intelligence levels of students on their algorithm design skills. This research was a descriptive study and carried out by survey methods. The sample consisted of 45 first-year educational faculty undergraduate students. The data was collected by using an algorithm skill test form (for this study [alpha]= 0.92) containing four open-ended algorithm questions, a scale on critical thinking disposition and levels (for this study [alpha] = 0.82), and a logico-mathematical intelligence self-perception scale ([alpha] = 0.72). It was found that students' logico-mathematical intelligence and critical thinking individually positively influence their algorithm design skills. According to a stepwise linear regression, these two predictors could respectively explain 54.7% and additionally 4.4% (59.7% in total) of the variance of algorithm design skill. (Contains 4 tables.)