Heterozygous loss-of-function (LoF) mutations in SETD1A, which encodes a subunit of histone H3 lysine 4 methyltransferase, have been shown to cause a novel neurodevelopmental syndrome and increase the risk for schizophrenia. To study the effect of decreased SETD1A function in human cells, we generated excitatory/inhibitory neuronal networks from human induced pluripotent stem cells with a SETD1A heterozygous LoF mutation (SETD1A+/-). Our data show that SETD1A haploinsufficiency resulted in altered neuronal network activity, which was mainly characterized by an overly synchronized network. In individual neurons, this network phenotype was reflected by increased somatodendritic complexity and elevated synaptic connectivity. We found that this network phenotype was driven by SETD1A haploinsufficiency in glutamatergic neurons. In accordance with the functional changes, transcriptomic profiling revealed perturbations in gene sets associated with schizophrenia, synaptic transmission and glutamatergic synaptic function. At the molecular level, we identified specific changes in the cAMP/PKA pathway pointing toward a hyperactive cAMP pathway in SETD1A+/- neurons. Finally, using pharmacological experiments targeting the cAMP pathway we were able to rescue the network deficits in SETD1A+/- cultures. In conclusion, our results illuminate key molecular, cellular and network abnormalities caused by SETD1A haploinsufficiency and demonstrate a direct link between SETD1A and the cAMP-dependent pathway in human neurons.