The zebrafish is extensively used as a model organism for studying several disorders of the central nervous system (CNS), including epilepsy. Some antiseizure drugs (ASDs) have been shown to produce discrepant results in larvae and adults zebrafish, therefore, their anticonvulsant efficacy in subsequent stages of the pentylenetetrazole (PTZ)-induced seizures should be more precisely characterized. The purpose of this study was to investigate behavioral effects of five classic ASDs: valproate (VPA), phenytoin (PHT), carbamazepine (CBZ), diazepam (DZP), and phenobarbital (PB) administered intraperitoneally (i.p.) in the PTZ-induced seizure test in adult zebrafish. We determined the time of maximal effect and the dose-response relationship of the studied ASDs. Furthermore, we assessed changes in the locomotor activity and the anxiety-like behavior in the color preference test. Moreover, drug concentrations in zebrafish homogenates were examined. VPA, DZP, and PB significantly increased the seizure latency at three subsequent stages of seizures (SI–SIII). PHT produced the anticonvulsant-like effect at SI and SII, while CBZ was effective at SII and SIII. Only DZP decreased zebrafish locomotor activity. A strong anxiolytic-like effect was observed after administration of PHT and PB. A weak anxiolytic-like effect occurred after treatment with VPA and DZP. The HPLC analysis showed the average concentrations of the studied ASDs in the fish body during the maximum anticonvulsant activity of each drug. Our results confirm the advantages of using zebrafish with the mature CNS over larval models and its utility to investigate some neuropharmacological properties of the tested drugs.