Background: There is a need for novel therapies for relapsed or refractory multiple myeloma, and B-cell maturation antigen (BCMA) is a validated target. Teclistamab is a bispecific antibody that binds BCMA and CD3 to redirect T cells to multiple myeloma cells. The aim of the MajesTEC-1 study was to evaluate the safety, tolerability, and preliminary efficacy of teclistamab in patients with relapsed or refractory multiple myeloma. Methods: This open-label, single-arm, phase 1 study enrolled patients with multiple myeloma who were relapsed, refractory, or intolerant to established therapies. Teclistamab was administered intravenously (range 0·3−19·2 μg/kg [once every 2 weeks] or 19·2−720 μg/kg [once per week]) or subcutaneously (range 80−3000 μg/kg [once per week]) in different cohorts, with step-up dosing for 38·4 μg/kg or higher doses. The primary objectives were to identify the recommended phase 2 dose (part one) and characterise teclistamab safety and tolerability at the recommended phase 2 dose (part two). Safety was assessed in all patients treated with at least one dose of teclistamab. Efficacy was analysed in response-evaluable patients (ie, patients who received at least one dose of teclistamab and had at least one post-baseline response evaluation). This ongoing trial is registered with ClinicalTrials.gov, NCT03145181. Findings: Between June 8, 2017, and March 29, 2021, 219 patients were screened for study inclusion, and 157 patients (median six previous therapy lines) were enrolled and received at least one dose of teclistamab (intravenous n=84; subcutaneous n=73). 40 patients were administered the recommended phase 2 dose, identified as once per week subcutaneous administration of teclistamab at 1500 μg/kg, after 60 μg/kg and 300 μg/kg step-up doses (median follow-up 6·1 months, IQR 3·6−8·2). There were no dose-limiting toxicities at the recommended phase 2 dose in part one. In the 40 patients treated at the recommended phase 2 dose, the most common treatment-emergent adverse events were cytokine release syndrome in 28 (70%; all grade 1 or 2 events) and neutropenia in 26 (65%) patients (grade 3 or 4 in 16 [40%]). The overall response rate in response-evaluable patients treated at the recommended phase 2 dose (n=40) was 65% (95% CI 48−79); 58% achieved a very good partial response or better. At the recommended phase 2 dose, the median duration of response was not reached. 22 (85%) of 26 responders were alive and continuing treatment after 7·1 months’ median follow-up (IQR 5·1−9·1). At the recommended phase 2 dose, teclistamab exposure was maintained above target exposure levels, and consistent T-cell activation was reported. Interpretation: Teclistamab is a novel treatment approach for relapsed or refractory multiple myeloma. At the recommended phase 2 dose, teclistamab showed promising efficacy, with durable responses that deepened over time, and was well tolerated, supporting further clinical development. Funding: Janssen Research & Development.