Amino acids having more number of amino groups than carboxyl groups are basic amino acids. Histidine has a 'NH' attached to 2 carbons and it is called basic amino acid. However, tryptophan (having >NH) is called neutral amino acid. Why is it so?
According to PubChem, indole (the nitrogen containing ring system of tryptophan) has a pKa value of -2.4. That means that it is a very weak base: at pH 0 (strong acid) it will be less than 1% protonated, and at neutral pH (physiological conditions) it will be neutral for all practical purposes. Notice that the indole nitrogen lone electron pair is conjugated as part of the pi system of the indole ring--hence it is unable to act as a base. The imidazole ring of histidine, which superficially resembles the indole group in tryptophan, has two nitrogens--one is similarly conjugated, but the other has a lone pair in the plane of the ring and is available to be protonated.