Variation in cognitive performance, which strongly predicts functional outcome in schizophrenia (SZ), has been associated with multiple immune-relevant genetic loci. These loci include complement component 4 (C4A), structural variation at which was recently associated with SZ risk and synaptic pruning during neurodevelopment and cognitive function. Here, we test whether this genetic association with cognition and SZ risk is specific to C4A, or extends more broadly to genes related to the complement system. Using a gene-set with an identified role in "complement" function (excluding C4A), we used MAGMA to test if this gene-set was enriched for genes associated with human intelligence and SZ risk, using genome-wide association summary statistics (IQ; N = 269 867, SZ; N = 105 318). We followed up this gene-set analysis with a complement gene-set polygenic score (PGS) regression analysis in an independent data set of patients with psychotic disorders and healthy participants with cognitive and genomic data (N = 1000). Enrichment analysis suggested that genes within the complement pathway were significantly enriched for genes associated with IQ, but not SZ. In a gene-based analysis of 90 genes, SERPING1 was the most enriched gene for the phenotype of IQ. In a PGS regression analysis, we found that a complement pathway PGS associated with IQ genome-wide association studies statistics also predicted variation in IQ in our independent sample. This association (observed across both patients and controls) remained significant after controlling for the relationship between C4A and cognition. These results suggest a robust association between the complement system and cognitive function, extending beyond structural variation at C4A.