In this work, we investigate the worldsheet symmetry of bosonic brane theories and its quantum consistency in the tensionless limit. We find that the residual worldsheet symmetry after specific gauge fixing is generated by a novel algebra, denoted as g⁽ᵖ⁾_λ. To achieve full quantization of the tensionless brane, we introduce a bc ghost system and derive the overall BRST charge. Moreover, we calculate the quantum anomaly of the g⁽ᵖ⁾_λ algebra for general parameters p and λ in the framework of canonical quantization. After demanding that this quantum anomaly vanishes, we derive the critical dimensions of the bosonic brane theories. Especially, we obtain nontrivial solutions for the tensionless string: D=14 spacetime dimensions when λ=-1 and D=26 spacetime dimensions when λ=1. We also notice that the quantum anomaly automatically vanishes after the Riemann zeta function regularization for p>1. This is consistent with the mathematical fact that there is no scalar central extension of the algebra g⁽ᵖ⁾_λ for p>1.