Comet 21P/Giacobini-Zinner was observed from Nov. 8 to Dec. 10, 1998. Pre- and post-perihelion CCD images of the gas (CN, C2) and dust (green and red continua) coma were obtained with the 82 cm IAC-80 telescope at Teide Observatory (Canary Islands, Spain). For vp =0.85 rH-0.5 and vd = 1.19 km s-1 (i.e. characteristic of HCN being the CN parent species), the CN column density profiles are best reproduced with parent and daughter lifetimes of the order of 19 300 and 256 000 s. An equally good reproduction of the observed profiles is achieved by considering that a mixture of nitrogen compounds expanding at vp =1 km s-1 and with a lifetime of 19 000 s produces CN with an ejection velocity of vd=2.5 km s-1 and a lifetime of 174 000 s. Fitting the observed CN profiles with variable velocities and lifetimes, the results indicate that the nature of the CN precursor in comet 21P/Giacobini-Zinner is still unclear, ruling out HCN as the only precursor and favouring a mixture of nitrogen compounds. Regarding C2, the derived lifetimes are 35 000 and 62 000 s, if the parent and daughter velocities are fixed at ~ 1 km s-1. Gas production rates derived by means of the Vectorial modeling with the mentioned above lifetimes and velocities indicate that (i) the comet activity decreases with decreasing rH (i.e. peak activity is not reached at the perihelion), and (ii) as already known, the comet is typically depleted in C2 with a log {QC_2/ QCN } ~ -0.4. The azimuthally averaged surface brightness profiles of the continuum images are well fitted with m >=1 in a log B - log rho representation at projected radial distances (rho ) larger than 1000 km. The continuum light scattered from the dust in the coma of comet Giacobini-Zinner is redder than the Sun light on every date from Nov. 8 to 24, regardless the cometocentric distance. On Nov. 25, there is a sudden change in the dust color, being considerably bluer than the Sun, whereas on Dec. 7 and 8, the dust became much redder than it was before. These color variations do not seem to be related to sudden variations (relative minimum or maximum) in the cometary activity. The gas-to-dust mass ratio is ~ 1, but affected by a large uncertainty (about a factor of 2) since the comet was not simultaneously imaged in the OH band, and the H2O production rate has been considered from other measurements taken some weeks before ours.