Alpaca (Lama pacos) is one of the two species of South American Camelids being Huacaya the most important breed due to its higher fibre production. Appropriate knowledge of genetic parameters for production traits is important in order to predict the selection response and also to establish selection strategies. The purpose of the present study is to estimate the genetic parameters and the fixed effects for fibre production in a population of Huacaya alpaca breed from the Toccra community (Arequipa region, Peru). The animal population consisted of 286 descendents, 38 sires and 188 dams. The analyses carried out showed that the effects of sex, colour and year of shearing were not significant while the age at shearing was significant on all traits. Fleece weight showed the highest heritability values while diameter and length fibre showed an intermediate value. Genetic and phenotypic correlations were all positive with high values between fibre diameter and length. Therefore, a promising panorama is depicted for a selection program as it will be possible to obtain a good response to the selection. © Medwell Journals, 2011.